Rotation of Axes in Two Dimensions

A rotation of axes in two dimensions is a mapping from an x y Cartesian coordinate system to a new coordinate system that keeps the origin fixed while the new axes are obtained by rotating the original x and y axes counterclockwise through an angle theta. A point keeps the same location in the plane but is described by different coordinates in the two systems, and in the new system that same point appears to have rotated in the opposite direction, clockwise through the same angle. The construction generalizes to a rotation of axes in more than two dimensions, and a rotation of axes is always a linear map and a rigid transformation.