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Appearance. 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.
Transformation matrix. In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . [citation needed] Note that has rows and columns, whereas the transformation is from to .
Rotation (mathematics) 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 rotation is a negative magnitude so ...
There are 3 representatives fixing {0, 1, ∞}, which are the three transpositions in the symmetry group of these 3 points: /, which fixes 1 and swaps 0 with ∞ (rotation by 180° about the points 1 and −1), , which fixes ∞ and swaps 0 with 1 (rotation by 180° about the points 1/2 and ∞), and / which fixes 0 and swaps 1 with ∞ ...
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
Version 2.0 of Google Maps Mobile was announced at the end of 2007, with a stand out My Location feature to find the user's location using the cell towers, without needing GPS. [193] [194] [195] In September 2008, Google Maps was released for and preloaded on Google's own new platform Android. [196] [197]
Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator[1] or WGS 84/Pseudo-Mercator is a variant of the Mercator map projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005. [2] It is used by virtually all major online map providers, including Google ...
Google Maps Bing Maps MapQuest Mapy.cz OpenStreetMap Here WeGo Apple Maps Yandex Maps; Degrees of motion Vertical, horizontal, depth, rotation (beta), 360 panoramic (Street View), 3D mode (Google Earth JavaScript) Vertical, horizontal, depth, 360 panoramic (Streetside), 3D mode (tilt, pan, rotate) Vertical, horizontal, depth