
 Coordinate rotation  (Site not responding. Last check: 20071105) 
  In other words, a rotation is a type of isometry – note however that there are isometries other than rotations, such as translations, reflections, and glide reflections. 
  In two dimensions, a counterclockwise rotation of the plane about the origin, where $(x,y)$ is mapped to $(x\text{'},y\text{'})$, is given by the same formulas as a coordinate transformation with a clockwise rotation of the coordinate axes, resulting in a change of coordinates $(x,y)$ into $(x\text{'},y\text{'})$: 
  This rotation is similar to a two dimensional rotation, except that instead of x and y axes, there are $\backslash mathbf\{u\_\backslash perp\}$ and $\backslash mathbf\{v\}\; \backslash times\; \backslash mathbf\{u\_\backslash perp\}$ axes, both of which are perpendicular to v. 
 www.grohol.com /psypsych/Coordinate_rotation (993 words) 
