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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 ...
Rotation of an object in two dimensions around a point O. 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. Rotation can have a sign (as in the sign of an angle ): a clockwise ...
Cardinal directions or cardinal points may sometimes be extended to include vertical position ( elevation, altitude, depth ): north and south, east and west, up and down; or mathematically the six directions of the x-, y-, and z-axes in three-dimensional Cartesian coordinates. Topographic maps include elevation, typically via contour lines .
The trace of a rotation matrix is equal to the sum of its eigenvalues. For n = 2, a rotation by angle θ has trace 2 cos θ. For n = 3, a rotation around any axis by angle θ has trace 1 + 2 cos θ. For n = 4, and the trace is 2(cos θ + cos φ), which becomes 4 cos θ for an isoclinic rotation.
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 ...
identity (identity; 1) rotation about an axis through a vertex, perpendicular to the opposite plane, by an angle of ±120°: 4 axes, 2 per axis, together 8 ((1 2 3), etc.; 1 ± i ± j ± k / 2 ) rotation by an angle of 180° such that an edge maps to the opposite edge: 3 ((1 2)(3 4), etc.; i, j, k) reflections in a plane perpendicular to ...
Google Street View is a technology featured in Google Maps and Google Earth that provides interactive panoramas from positions along many streets in the world. It was launched in 2007 in several cities in the United States, and has since expanded to include all of the country's major and minor cities, as well as the cities and rural areas of many other countries worldwide.