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A 180° rotation (middle) followed by a positive 90° rotation (left) is equivalent to a single negative 90° (positive 270°) rotation (right). Each of these figures depicts the result of a rotation relative to an upright starting position (bottom left) and includes the matrix representation of the permutation applied by the rotation (center ...
In computer science, the lexicographically minimal string rotation or lexicographically least circular substring is the problem of finding the rotation of a string possessing the lowest lexicographical order of all such rotations. For example, the lexicographically minimal rotation of "bbaaccaadd" would be "aaccaaddbb".
Note that if φ is increased by a full rotation of 360 degrees, the arguments of sine and cosine only increase by 180 degrees. The resulting parameters are the opposite of the original values, (−a, −b, −c, −d); they represent the same rotation.
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 .
These equations can be proved through straightforward matrix multiplication and application of trigonometric identities, specifically the sum and difference identities.. The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group.
Every year, celebrities try to capitalize on the holiday season by releasing festive music. Singers like Mariah Carey, Ariana Grande, and Michael Bublé managed to perfect the cheesy art form.
If you have had trouble saving for retirement, putting money away for a down payment, creating a budget, saving for family vacation or other money goals, don't feel too bad, said Brad Klontz, a...
An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres ...