In two dimensions, consider a reference frame with basis vectors:
Ā .
The reference frame is rotated counter-clockwise through and angle Ā Ā , obtaining a new reference frame with basis Ā .The components Vx and Vy in the Ā Ā basis of a generic vector Ā are transformed according to the rotation matrix
Ā Ā Ā .
1) Express the component of the vector Ā in the Ā basis
2) Express how the sets of basis vectors transform. That is, express the vectors Ā as a function of the vectors Ā and vice-versa.