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  2. Rotation (mathematics) - Wikipedia

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

    The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...

  3. Plane-based geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Plane-based_geometric_algebra

    The center of the picture is a point that is performing a point reflection on the tetrahedron. In 3D plane-based GA, points 3-reflections. Algebraically this means they are grade-3 – but their geometric interpretation is very different from the usual geometric interpretation of a "trivector" as an "oriented volume element".

  4. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...

  5. 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 .

  6. Orientation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Orientation_(geometry)

    The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix. The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real ...

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  8. Circular motion - Wikipedia

    en.wikipedia.org/wiki/Circular_motion

    Figure 1: Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangential to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation. Figure 2: The velocity vectors at time t and time t + dt are moved from the orbit on the left ...

  9. List of primary education systems by country - Wikipedia

    en.wikipedia.org/wiki/List_of_primary_education...

    In second and third grade students are assessed on subjects including Latvian language, minority language, math, and foreign languages and are graded using the 10 point scale. In fourth grade through ninth grade students begin being assessed in all subject areas and are graded using the 10 point scale.

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