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Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates ( x, y) with respect to the ...
Clockwise. Two-dimensional rotation can occur in two possible directions or senses of rotation. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock 's hands relative to the observer: from the top to the right, then down and then to the left, and back up to the top. The opposite sense of rotation or revolution is (in ...
Earth's rotation. Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise . The North Pole, also known as the Geographic North ...
The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith. An azimuth ( / ˈæzəməθ / ⓘ; from Arabic: اَلسُّمُوت, romanized : as-sumūt, lit. 'the directions') [1] is the ...
Google Maps is available as a mobile app for the Android and iOS mobile operating systems. The first mobile version of Google Maps (then known as Google Local for Mobile) was launched in beta in November 2005 for mobile platforms supporting J2ME. [184] [185] [186] It was released as Google Maps for Mobile in 2006. [187]
Google Translate is a web-based free-to-use translation service developed by Google in April 2006. [11] It translates multiple forms of texts and media such as words, phrases and webpages. Originally, Google Translate was released as a statistical machine translation (SMT) service. [11] The input text had to be translated into English first ...
Optical activity is reciprocal, i.e. it is the same for opposite directions of wave propagation through an optically active medium, for example clockwise polarization rotation from the point of view of an observer. In case of optically active isotropic media, the rotation is the same for any direction of wave propagation.