Rotation of axes in two dimensions

In mathematics, a rotation of axes in two dimensions is a mapping from an x y {\displaystyle xy} -Cartesian coordinate system to an x ′ y ′ {\displaystyle x'y'} -Cartesian coordinate system in which the origin is kept fixed and the x ′ {\displaystyle x'} and y ′ {\displaystyle y'} axes are obtained by rotating the x {\displaystyle x} and y {\displaystyle y} axes counterclockwise through an angle θ {\displaystyle \theta } . A point P {\displaystyle P} has coordinates ( x , y ) {\displaystyle (x,y)} with respect to the original system and coordinates ( x ′ , y ′ ) {\displaystyle (x',y')} with respect to the new system.

Source: Wikipedia — Rotation of axes in two dimensions (CC BY-SA 4.0)