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  2. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    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 ...

  3. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    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 .

  4. Rotation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rotation_(mathematics)

    Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. 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 ...

  5. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    The azimuth angle θ appears to equal positive 90°, as rotated counterclockwise from the azimuth-reference x–axis; and the inclination φ appears to equal 30°, as rotated from the zenith–axis. (Note the 'full' rotation, or inclination, from the zenith–axis to the y–axis is 90°).

  6. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axis–angle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  7. Rotation - Wikipedia

    en.wikipedia.org/wiki/Rotation

    A sphere rotating (spinning) about an axis. Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation.A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.

  8. Dying To Be Free - The Huffington Post

    projects.huffingtonpost.com/dying-to-be-free...

    The last image we have of Patrick Cagey is of his first moments as a free man. He has just walked out of a 30-day drug treatment center in Georgetown, Kentucky, dressed in gym clothes and carrying a Nike duffel bag.

  9. Clockwise - Wikipedia

    en.wikipedia.org/wiki/Clockwise

    For example, the daily rotation of the Earth is clockwise when viewed from above the South Pole, and counterclockwise when viewed from above the North Pole (considering "above a point" to be defined as "farther away from the center of earth and on the same ray"). The shadow of a horizontal sundial in the Northern Hemisphere rotates clockwise