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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. [2] [3] A rotation of axes is a linear map [4] [5] and a rigid transformation.
The reason for the clockwise standard for most screws and bolts is that supination of the arm, which is used by a right-handed person to tighten a screw clockwise, is generally stronger than pronation used to loosen. Sometimes the opposite (left-handed, counterclockwise, reverse) sense of threading is used for a special reason.
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 ...
A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops ...
where for every direction in the base space, S n, the fiber over it in the total space, SO(n + 1), is a copy of the fiber space, SO(n), namely the rotations that keep that direction fixed. Thus we can build an n × n rotation matrix by starting with a 2 × 2 matrix, aiming its fixed axis on S 2 (the ordinary sphere in three-dimensional space ...
This definition is independent of the object's direction of rotation about its axis. This implies that an object's direction of rotation, when viewed from above its north pole, may be either clockwise or counterclockwise. The direction of rotation exhibited by most objects in the solar system (including Sun and Earth) is counterclockwise.
The Riemann Hypothesis. Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize ...
Retrograde orbit: the satellite (red) orbits in the direction opposite to the rotation of its primary (blue/black) Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object (right figure).