Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire (n − 1)-dimensional flat of fixed points in a n-dimensional space.
Mathematically, a rotation is a map. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation which if applied to the frame of reference results in the body being at the same coordinates. For example, in two dimensions rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise about the same point while the body is kept fixed. These two types of rotation are called active and passive transformations.
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.
In his review for AllMusic, Alex Henderson says that "this CD doesn't quite fall into the 'essential' category... Nonetheless, Geometry is an enjoyable release that Perelman's more-devoted followers will want."
The Penguin Guide to Jazz notes that "Bergman is wily enough to find ways of both supporting and undercutting the mighty sound of the tenor."
Geometry is the second album by electronic musician Jega, released in 2000 on the Planet Mu label.
In medical education, a clerkship, or rotation, refers to the practice of medicine by medical students (M.D. or D.O.) during their final year(s) of study. Traditionally, the first half of medical school trains students in the classroom setting, and the second half takes place in a teaching hospital. Clerkships give students experiences in all parts of the hospital setting, including the operating room, emergency department, and various other departments that allow learning by viewing and doing.
During this training, students are required to rotate through different medical specialties and treat patients under the supervision of physicians. Students elicit patient histories, complete physical examinations, write progress notes, and assist in surgeries and medical procedures. The work hours are that of a full-time job, generally similar to that of residents. Students may also be required to work on weekends and to be on call.
In the United States, medical school typically lasts four years. Medical students spend the third and fourth years rotating through a combination of required clerkship and electives. Most medical schools require rotations in internal medicine, surgery, pediatrics, psychiatry, obstetrics and gynecology, family medicine, radiology, and neurology. Some schools additionally require emergency medicine and intensive-care medicine. Furthermore, a common graduation requirement is to complete a sub-internship in a specialty, where the medical student acts as an intern.
DS2 (abbreviation of Dirty Sprite 2) is the third studio album by American hip hop recording artist Future. The album was released on July 17, 2015 by A1, Freebandz and Epic Records. The album serves as the sequel from his breakout mixtape Dirty Sprite (2011). The album was supported by four singles "Fuck Up Some Commas", "Real Sisters", "Blow a Bag" and "Where Ya At" featuring Drake.
Upon its release, DS2 received generally positive reviews from critics and was ranked as one of the best albums of 2015 by several publications. It debuted at number one on the US Billboard 200 and sold 126,000 copies in its first week. The album has since been certified Gold by the Recording Industry Association of America (RIAA). As of February 2016, the album has sold 344,000 in the United States.
On July 10, 2015, Future posted the artwork and announced his new album, titled DS2, would be released on July 17, 2015. The tracklist of the album was released on July 15, 2015. In an interview with Power 105.1, he explained the official album title was abbreviated to DS2 in order to avoid copyright infringement from Sprite.
In aviation, rotation refers to the action of applying back pressure to a control device, such as a yoke, side-stick or centre stick, to lift the nose wheel off the ground during the takeoff roll. Proper rotation is important for safety reasons and to decrease takeoff distance. Rotation occurs when the aircraft lifts up from the runway and takes off once it reaches the optimal speed for a safe takeoff, which is called the VR speed. Certain airplanes like Boeing 727, Boeing 767, and Concorde require a high degree of rotation during takeoff, but not all airplanes require this degree of rotation. If too much rotation is added for takeoff, the airplane can face a tailstrike, or, in the worst case, will stall and crash.
Rotation is a flight concept which is integral to the design of many tricycle gear aircraft and is not applicable to conventional gear aircraft. At the design phase in tricycle gear aircraft there is a selection of the on ground angle of attack of the wing. This angle is created in the mains and nose gear leg length design which creates a negative angle of attack relative to the ground. The effect of this is that during the takeoff roll the wing will have negative lift until the pilot commands the nose skyward to create a positive angle of attack of the wing. At the end of the flight the concept is reversed where at touchdown all tires touch the runway and the wing is instantly moved to a negative angle of attack which causes the wing to stop lifting. At one time Cessna Aircraft featured this idea as "Land O Matic" so noted on all of their tricycle gear aircraft.