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R2

R2 may refer to: For other uses, see [[R2 (disambiguation)]].

Entertainment

R2-D2

is a fictional astromech droid character in the Star Wars franchise, created by filmmaker as a resourceful companion central to the saga's narrative. First appearing in the 1977 film Star Wars (later subtitled A New Hope), the character is depicted with a distinctive blue-and-white cylindrical body topped by a dome-shaped head, communicating exclusively through a series of beeps, whistles, and electronic sounds that convey emotions and information. Throughout the franchise, R2-D2 serves key figures including Queen Padmé Amidala, Jedi Knight Anakin Skywalker, and Rebel hero Luke Skywalker, demonstrating loyalty and ingenuity in critical moments. In the original trilogy, R2-D2 delivers the stolen Death Star plans to Princess Leia Organa and assists Luke during the Battle of Yavin by providing targeting data that enables the station's destruction. The droid also repairs the Millennium Falcon's hyperdrive during the events of The Empire Strikes Back and supports the Rebel strike team on Endor in Return of the Jedi. In the prequel trilogy, R2-D2 aids Anakin in repairing the royal starship during the Battle of Naboo and participates in Clone Wars engagements alongside Jedi forces. The character returns in the sequel trilogy, joining the Resistance to help locate Luke Skywalker and contributing to efforts against the First Order, including further maintenance on the Millennium Falcon. R2-D2's vocalizations were crafted by sound designer , who synthesized them from recordings of his own distorted voice, a baby's cry, and an elephant's trumpeting to create an expressive, non-verbal language that audiences intuitively understand. The droid has achieved significant cultural impact as a symbol of mechanical heroism, inspiring widespread merchandise such as action figures released by Kenner starting in 1978, which became bestsellers and helped launch the franchise's merchandising empire. R2-D2 frequently partners with the protocol droid , forming a longstanding comedic duo that highlights themes of friendship across the human-droid divide. The character continues to appear in Star Wars spin-offs, including a notable role alongside in the 2020 second season finale of , The Book of (2021), and Obi-Wan (2022). In-universe, R2-D2 measures 0.96 meters in height and is equipped with versatile tools for repair and navigation, including a torch for fusing metal, a retractable for , and boosters enabling short flights and escapes. Additional features encompass multiple manipulator arms, a cargo bay for small items, and computer interface ports for hacking and data transfer, making the droid indispensable in operations and scenarios.

Science and technology

Coefficient of determination

The , denoted as R^2, quantifies the proportion of the variance in the dependent variable that is explained by the independent variables in a model, with values ranging from 0 to 1, where 0 indicates that the model explains none of the variability and 1 indicates a perfect fit. The concept was introduced by in 1921 in the context of path analysis for multiple models. This measure is particularly useful in assessing the for models, as it provides a standardized way to evaluate how well the predicted values align with the observed data. The formula for R^2 is given by R^2 = 1 - \frac{SS_{res}}{SS_{tot}}, where SS_{res} is the , calculated as \sum (y_i - \hat{y}_i)^2 (the sum of squared differences between observed values y_i and predicted values \hat{y}_i), and SS_{tot} is the , calculated as \sum (y_i - \bar{y})^2 (the sum of squared differences between observed values and the mean \bar{y}). To compute R^2 in , first fit the model to estimate the regression line, then derive the predicted values, compute SS_{res} and SS_{tot}, and substitute into the formula. Interpretation of R^2 depends on context, with values above 0.7 often signaling a strong model fit in physical sciences like physics, though lower thresholds (e.g., 0.3–0.5) may be acceptable in and other social sciences due to inherent data variability. To address potential inflation from adding irrelevant predictors, the adjusted R^2 penalizes model complexity using the formula \text{Adjusted } R^2 = 1 - \left[ (1 - R^2) \frac{n - 1}{n - k - 1} \right], where n is the sample size and k is the number of predictors; for instance, if R^2 = 0.8, n = 20, and k = 2, the adjusted value is approximately 0.77, providing a more conservative estimate. In , R^2 evaluates models variables like GDP growth or , while in , it assesses algorithms such as linear models for tasks like price prediction, though it remains a key metric in frameworks like for . A critical caveat is that high R^2 values indicate strong association but do not imply causation, as spurious correlations can arise without underlying mechanisms, a principle upheld in statistical standards through 2025 emphasizing complementary tests like residual analysis for .

Computing

Radare2, commonly abbreviated as r2, is an open-source framework for binaries, providing tools for disassembly, , patching, and forensics. It originated from the radare project, initiated in 2006 by developer Sergi Àlvarez for tasks like file recovery from HFS+ disks, and was refactored and forked into in 2009 to address limitations and enhance . This evolution introduced greater flexibility, enabling easier scripting and integration with external tools, which has made it a staple in and software security research. Key features of include its embedded scripting capabilities through a custom command language and the , which allows and control from languages like , , or even embedded JavaScript interpreters. It supports disassembly and analysis for over 70 architectures, including x86, , , and , facilitating cross-platform binary examination. For binary analysis workflows, users typically start by loading a file with the r2 command (e.g., r2 sample.exe), followed by aaa to perform recursive analysis of functions and symbols, and pdf to print disassembled code at the current ; these commands enable rapid identification of code structures without graphical interfaces. Graphical support comes via Iaito, the official forked from the earlier project around 2021 amid community splits, with significant updates by 2023 improving visualization of graphs and decompilation. As of 2025, maintains an active development community, with regular releases—such as version 6.0.4 in September 2024—and ongoing contributions via , including plugins for advanced tasks like integration for dynamic instrumentation. The project hosts annual events like r2con since 2016 and fosters collaboration through channels like and Telegram, ensuring it remains a vital, libre for low-level tasks. The .r02 file extension denotes the third volume in multi-part RAR archives, a proprietary compression format developed by Eugene Roshal in 1993 for efficient data archiving and splitting of large files. In this scheme, oversized archives are divided into sequential volumes—starting with .r00 for the first part, .r01 for the second, and .r02 for the third—to facilitate storage on limited media or network transfers, with each volume containing compressed blocks that must be recombined for extraction. The format supports error correction and higher compression ratios than ZIP, making it suitable for software distribution and backups. To extract .r02 files, all preceding volumes (.r00 through .r01) are required, as the archive is incomplete without them; compatible tools include the official software, which handles creation and unpacking natively, or open-source alternatives like that support reading without proprietary licensing. Users initiate by selecting the first volume (.r00) in the tool, which automatically detects and processes subsequent parts like .r02, restoring the original files while verifying integrity. This multi-volume approach remains relevant in 2025 for handling terabyte-scale datasets in computing environments.

Mathematics

In mathematics, \mathbb{R}^2 denotes the Euclidean 2-dimensional space, also known as the Cartesian plane, consisting of all ordered pairs of real numbers (x, y) where x, y \in \mathbb{R}. This space is equipped with the standard Euclidean metric d((x_1, y_1), (x_2, y_2)) = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}, which induces the usual topology on the plane and corresponds to the straight-line distance between points. The concept originated in 19th-century analytic geometry, independently developed by and around 1637, who introduced coordinates to unify algebra and geometry by representing points as pairs on perpendicular axes. Unlike \mathbb{R}, the 1-dimensional real line representing points along a single axis, \mathbb{R}^2 captures planar geometry with two independent coordinates, enabling the study of areas, curves, and transformations not possible in one dimension. This structure extends to \mathbb{R}^n for higher dimensions, but \mathbb{R}^2 exhibits unique properties, such as the Jordan curve theorem, which states that any simple closed curve in \mathbb{R}^2 divides the plane into two connected components: a bounded interior and an unbounded exterior, with the curve serving as the boundary of both. As a vector space over \mathbb{R}, \mathbb{R}^2 has dimension 2, with the standard basis vectors \mathbf{i} = (1, 0) and \mathbf{j} = (0, 1), allowing any vector (x, y) to be expressed as the linear combination x\mathbf{i} + y\mathbf{j}. In linear algebra, this facilitates operations like matrix transformations and inner products, foundational for solving systems of equations geometrically. In calculus, functions f: \mathbb{R}^2 \to \mathbb{R} support partial derivatives \frac{\partial f}{\partial x} and \frac{\partial f}{\partial y}, which analyze directional changes, while double integrals \iint_D f(x,y) \, dA compute volumes under surfaces or areas of regions D \subset \mathbb{R}^2. For instance, Green's theorem relates a line integral around the boundary \partial D to a double integral over D: \iint_D \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) dA = \oint_{\partial D} P \, dx + Q \, dy, enabling area calculations via \iint_D dA = \frac{1}{2} \oint_{\partial D} -y \, dx + x \, dy.

Transportation

Rail vehicles

The R2 class freight electric locomotives were a key component of the New York Central Railroad's (NYC) electrified freight operations in the early 20th century, designed specifically for high-density urban and tunnel service in the New York area. Built by a collaboration between the American Locomotive Company (ALCO) and General Electric (GE) between 1930 and 1931, the class comprised 42 units numbered 1202–1243. These locomotives adopted a C-C wheel arrangement, delivering 3,000 horsepower from four 750-horsepower traction motors, with a starting tractive effort of 66,600 pounds and a top speed of 60 mph. Measuring 54 feet in length and weighing 266,400 pounds, they were optimized for the 660-volt DC third-rail system, featuring advanced electric control systems for smooth acceleration in confined spaces like the Park Avenue tunnels. Following the experimental R-class prototypes introduced in , the R2 class addressed the limitations of earlier steam and early electric locomotives by providing reliable, smoke-free power for freight through 's congested corridors. They primarily operated in the NYC's New York Electrified Zone, including the and divisions, hauling , merchandise, and freight trains. In the 1940s, several units were reassigned to the Tunnel service, where they facilitated cross-border traffic between and . The design incorporated safety enhancements, such as improved and robust pantograph alternatives for potential overhead wire use, responding to earlier electrification incidents like derailments and power failures in the that highlighted the need for better traction control in wet or high-load conditions. In 1955, ten R2 locomotives were sold to the Chicago, South Shore and South Bend Railroad (CSS&SB), where seven were rebuilt with pantographs for 1,500-volt DC overhead catenary operation and renumbered 701–707. These units served on the South Shore Line's interurban freight and passenger services until their retirement in 1976, with the last examples scrapped by the early 1980s. The original NYC fleet was gradually withdrawn during the 1950s as diesel-electric locomotives took over, with all units scrapped by the early 1960s amid the NYC's financial decline leading to the 1968 merger into Penn Central. No R2 locomotives survive in preservation, though their engineering influenced subsequent classes like the Pennsylvania Railroad's GG1 and freight electrics, emphasizing durable components in underbodies for resistance in humid environments. Outside North America, the designation R2 also applies to modern regional rail vehicles, such as the New South Wales (NSW) Transport R sets in Australia. The R2 is the second unit in the fleet of bi-mode multiple units built by CAF for NSW TrainLink's long-distance regional services, introduced in 2024–2025 to replace aging XPT and Xplorer trains. These diesel-electric and electric-capable trains feature stainless steel construction, air conditioning, and improved passenger amenities like wider seating and accessibility features, operating on lines including the Central Coast and Blue Mountains routes with speeds up to 160 km/h. As of November 2025, R2 has undergone testing on the Richmond Line and is slated for full revenue service in early 2026, contributing to safety upgrades post-2010s incidents through advanced collision avoidance systems.

Road and urban transport

In across various U.S. cities, R2 zoning designates low- to moderate-density residential districts primarily intended for single-family homes and duplexes, promoting stable neighborhoods while allowing limited multi-family development. This classification emerged as part of the broader adoption of codes in the , following the U.S. Supreme Court's 1926 affirmation of zoning's constitutionality in Village of Euclid v. Ambler Realty Co., which encouraged municipalities to implement district-based regulations to separate incompatible developments. In , for instance, the R2 Two-Family Zone permits duplexes on lots with a minimum width of 50 feet and area of 5,000 square feet, with at least 2,500 square feet per dwelling unit, fostering incremental growth in established areas. Similar provisions exist in other cities, such as , where R2 allows single-household or duplex structures up to 35 feet in height, ensuring compatibility with surrounding single-family neighborhoods. Building height limits in R2 districts typically cap at 35 feet to maintain a suburban scale, though variations occur based on local codes; for example, , enforces this limit for duplexes to preserve visual harmony and light access. These regulations, rooted in early 20th-century efforts to control , have evolved through state-mandated incentives. In , 2024 updates to the Zoning Code via the Citywide Housing Incentive Program expanded density bonuses for qualifying projects in R2 and similar zones, allowing up to 120% additional units and floor area ratio increases of 55% when incorporating , aiming to address supply shortages without altering core district purposes. Such bonuses, drawn from California's Density Bonus Law, require concessions like reduced setbacks or parking in exchange for on-site affordable units, directly applying to R2 developments. R2 designations also appear in urban bus routing for enhanced transit corridors. In Metro Vancouver, , the R2 Marine Drive RapidBus operates as a high-capacity express service connecting to Phibbs Exchange, with extensions planned to Metrotown by 2027, running every 8 minutes during rush hours to accommodate up to 1,650 passengers per hour using articulated buses. This route integrates seamlessly with rail systems, linking to at Brentwood Town Centre and at Lonsdale Quay for transfers to , improving overall network efficiency and reducing reliance on private vehicles in dense urban areas. The service employs dedicated bus lanes and priority signals to achieve speeds comparable to , serving as a model for scalable road-based transit in growing suburbs. Policy impacts of R2 zoning on housing affordability stem from its density controls, which historically restricted supply and contributed to rising costs, but recent reforms mitigate this through streamlined approvals and incentives. In , Assembly Bill 2011 (the Affordable Housing and High Road Jobs Act of 2022), amended by AB 2243 in 2025, facilitates ministerial approval for multifamily projects on underutilized sites adjacent to R2 residential zones, enabling up to 30 units per and requiring prevailing wages to support . These updates, effective January 1, 2025, expand eligibility for density bonuses beyond traditional residential zones like R2, allowing more units in mixed-use contexts to boost —potentially adding thousands of below-market-rate homes statewide—while preserving neighborhood character. By overriding certain local restrictions, AB 2011 indirectly alleviates pressure on R2 districts, promoting equitable access to near transit corridors.

Vehicles

Automobiles and road vehicles

The is a manufactured by Subaru from 2003 to 2010 exclusively for the Japanese market, serving as the successor to the in the company's compact urban vehicle lineup. It featured a with a 658 cc inline-four gasoline engine compliant with kei car regulations, producing 45 to 53 horsepower in naturally aspirated form and up to 63 horsepower in turbocharged variants like the typeS model equipped with a (CVT). The design emphasized a compact, egg-shaped body with rounded corners, slim headlights, and a high-mounted taillight setup on the D-pillars, measuring approximately 3.4 meters in length to fit urban parking needs. Production ended in 2010 amid shifting consumer preferences toward larger vehicles and stricter emissions standards in the kei segment. The ORA R2, also known as the ORA 03 or Good Cat in various markets, is a battery-electric city car developed by Great Wall Motor's ORA sub-brand and launched in in 2020, with international exports beginning in 2023. It adopts a distinctive cat-themed styling inspired by retro designs like the , featuring rounded headlights resembling feline eyes, a compact silhouette, and playful interior accents, making it popular for urban commuting in densely populated cities. The vehicle is powered by a 47.8 kWh (LFP) battery offering up to 310 miles of range on the Chinese CLTC cycle, with a base price starting under $10,000 in to appeal to budget-conscious buyers. For the 2025 model year, updates include improved battery efficiency and enhanced basic ADAS features like and lane-keeping assist, without integration. Rivian unveiled the R2 in March 2024 as a mid-size electric SUV aimed at broadening the company's portfolio beyond the larger R1T and R1S models, with production now slated to begin in late 2026 at its Normal, Illinois facility following supply chain delays announced in 2025. Targeted at a starting price of around $45,000 before incentives, it addresses the demand for more affordable electric vehicles while maintaining Rivian's focus on adventure-oriented performance. The R2 offers over 300 miles of EPA-estimated range from dual battery pack options, seats five passengers standard with potential for seven via an optional third row, and supports bidirectional charging for vehicle-to-home power export. Design highlights include a bold, aerodynamic profile with flush door handles and a minimalist interior, paired with off-road capabilities such as available all-wheel drive, coil-spring suspension for varied terrain handling, and up to 0-60 mph acceleration in under three seconds in tri-motor configurations. Reservations opened immediately upon announcement with a $100 refundable deposit, with over 100,000 reservations as of mid-2025, reflecting strong early interest following the R1T's success in the premium EV truck segment.

Aircraft

The Polikarpov R-1 and R-2 were Soviet multi-purpose biplanes developed as licensed copies of the and DH.9 bombers, with production beginning in 1923 under the supervision of at GAZ-1 and later at GAZ-10 in . These featured a single M-5 engine rated at 295 kW (approximately 400 hp), a wingspan of 14 meters, and a maximum speed of 200 km/h, enabling a range of 700 km and a service ceiling of 5,000 meters while carrying two crew members, dual machine guns, and up to 200 kg of bombs. Over 2,800 units were produced between 1924 and 1931, with early models using imported parts before full domestic manufacturing; they proved reliable in long-distance flights, such as Mikhail Gromov's 1925 Moscow-Peking-Tokyo , and were exported in small numbers to countries like . The R.2 was an two-seat reconnaissance introduced in 1918, marking the first branded under following its acquisition of Ansaldo designs. Designed by Celestino Rosatelli, it utilized a 300 hp A.12 liquid-cooled inline engine, achieved a maximum speed of 175 km/h at sea level, and had a wingspan of 12.3 meters, serving primarily in the for observation duties with a crew of two. A total of 129 examples were built, remaining in frontline service until 1925 as Italy transitioned to more advanced monoplanes. The was a experimental prototype developed in 1917 as part of the (giant aircraft) program, featuring an innovative design scaled up from a single-engine with four 260 hp D.IVa engines mounted internally in pairs to drive a single large tractor propeller via a central gearbox. Constructed primarily of wood with fabric covering and a forward , it boasted a of 42.16 meters, a length of 20.32 meters, and an estimated maximum speed of 130 km/h, with a potential of up to 30 hours when adjusted for crew and fuel loads. Only the sole prototype (R 55/17) flew after the in late 1918, demonstrating the ability to operate on just two engines, though further development was halted due to the war's end. The R.II was a German completed in by Deutsche Flugzeug-Werke, evolving from the earlier R.I as a larger four-engine design intended for long-range strategic operations during the final stages of . It employed a with two rear-mounted propellers driven by four 260 hp engines, a of 35 , a length of 21 , and a top speed of 132 km/h, allowing for up to six hours of flight while armed with multiple machine guns and a 800 kg bomb load. Only one example was constructed as the T 26-II, with testing limited by the and no series production undertaken.

Naval and military vehicles

The USS R-2 (SS-79) was an of the , laid down on 16 October 1917 by the Fore River Shipbuilding Company in , launched on 23 September 1918, and commissioned on 24 January 1919. Displacing approximately 600 tons on the surface and 680 tons submerged, it featured a length of 186 feet, a beam of 18 feet, and was armed with four 21-inch torpedo tubes forward along with one 3-inch deck gun. The vessel conducted training operations and patrols primarily in , including winter maneuvers in the from 1919 to 1920 and summer exercises off southern , before transferring to in June 1941 for sonar school duties and defensive patrols during ; it was decommissioned on 10 May 1945 and stricken from the on 2 June 1945. The Zest (R02) was a Z-class of the British Royal Navy, ordered on 12 February 1942 from in , launched on 14 October 1943, and completed on 20 July 1944. Armed with four 4.7-inch QF Mark IX guns in twin turrets, two 40-barrel 2-pounder "" anti-aircraft mountings, eight 20 mm Oerlikon guns, and eight 21-inch tubes in two quadruple launchers, it served in operations including Arctic convoys and the invasion of in 1945, earning battle honors for those campaigns. Post-war, Zest underwent conversion to a Type 15 fast anti-submarine frigate between 1956 and 1958 and participated in the as part of British naval contributions to forces, conducting patrols and escort duties off the Korean from 1950 to 1953; it was placed in reserve in July 1968, sold for scrap in 1969, and broken up on 18 July 1970. The Panzer 35(t) R-2 was the Romanian Army's designation for the Czechoslovak LT vz. 35 light tank, with 126 units ordered from Škoda Works on 14 August 1936 as part of a modernization program, the first 15 delivered in April–May 1937 and the remainder from late 1938 onward. Equipped with a 37 mm Škoda ÚV vz. 34 main gun and machine guns, the R-2 featured armor ranging from 8 to 25 mm thick, providing protection against light anti-tank weapons, and was powered by a 120 horsepower Škoda T-11 engine for a top speed of 35 km/h on roads. These tanks formed the backbone of Romania's 1st Armored Regiment during World War II, seeing combat in the Balkans campaign of 1941 as Axis forces advanced through the region, as well as later operations on the Eastern Front including the Battle of Odessa and the 1942 Stalingrad counter-offensive, where their mobility supported infantry advances but vulnerabilities to heavier Soviet armor became evident. Group R R2 is a subclass within the FIA's Group R rally car regulations, introduced in 2012 to standardize production-derived vehicles for international by replacing older and categories, with no new homologations allowed for those groups after 2013. Defined under FIA Appendix J Article 260, R2 specifies four-wheel-drive cars with turbocharged engines of up to 1.6 liters displacement, limited modifications for safety and performance equality, and a minimum production run of 2,500 units, distinguishing it from R1 (two-wheel-drive equivalents) and R3 (naturally aspirated two-wheel-drive up to 2.0 liters). Representative examples include the Peugeot 208 R2 and Ford Fiesta R2, which compete in regional and national rallies emphasizing close-to-stock drivetrains and turbo setups to maintain accessibility for teams.

Other uses

Education and classifications

In the Carnegie Classifications of Institutions of Higher Education, the R2 designation refers to "Doctoral Universities – High research activity," a category that recognizes institutions awarding at least 20 research or scholarship doctorates annually and expending a minimum of $5 million on research and development activities in the fiscal year. This classification, part of the 2025 Research Activity Designations released on February 13, 2025, by the in partnership with the Carnegie Foundation, emphasizes a balanced commitment to doctoral production and funding without the more stringent thresholds of higher tiers. The R2 category was introduced in the 2021 Carnegie update, which restructured the previous tiered system of research universities into a more data-driven framework focused on doctorate output and research spending, replacing older designations like "Research Universities (high research activity)." The 2025 iteration expanded the list to 139 R2 institutions, reflecting growth in research capacity across diverse U.S. sectors and prioritizing equitable metrics for production alongside financial investment. Notable examples of universities newly attaining R2 status in 2025 include San José State University, which achieved the designation through sustained growth in and research, and , recognized for its advancements in doctoral programs and interdisciplinary scholarship. Attaining R2 status carries significant implications for institutional and resource access, often facilitating eligibility for federal grants, enhanced partnerships, and of faculty and students, as it signals a robust . In contrast to the R1 category—"Doctoral Universities – Very high research activity," which requires at least 70 research doctorates and $50 million in expenditures—R2 highlights high but more accessible levels of activity, enabling mid-tier to compete for funding without the scale demanded of elite research powerhouses.

Standards and geography

The R2 Standard, also known as Responsible Recycling, is a certification program developed by Sustainable Electronics Recycling International (SERI) to promote ethical and sustainable practices in the recycling industry. Launched in 2008, it provides a for organizations handling used , focusing on , refurbishment, materials recovery, and final disposition while prioritizing , worker safety, and data destruction. The standard's current iteration, R2v3, was released in July 2020 and approved as an American National Standard by ANSI, incorporating rigorous audit requirements for —such as verified destruction of sensitive information—and environmental , including proper of hazardous materials and emissions controls. Unlike more restrictive certifications like e-Stewards, R2 permits exports of non-hazardous to certified downstream processors in any country, provided they adhere to equivalent standards, enabling broader flexibility while still prohibiting direct exports to non-compliant or unsafe destinations. As of 2025, more than 1,250 facilities worldwide hold R2 certification, with significant concentrations in (particularly the ), , and growing adoption in and , reflecting the standard's role in addressing the global e-waste crisis that generates over 62 million metric tons annually. This geographic distribution supports localized , reducing transportation emissions and ensuring compliance with international treaties like the on transboundary movements.