Cartesian reference systems rotation

Question

I have 2 cartesian reference systems A and B with the same origin and I know the axes versors of both of them. I have some points on A (Pa1, Pa2, ...) and I must rotate A (and Pa1, Pa2, ..) until A=B and get the new coordinations of Pa1, Pa2,...

Could someone tell me how it is possible to do this?

Answer 1

Form a matrix by taking the versors of $B$ in the basis of $A$. This matrix is the rotation matrix that applies $A$ to $B$. (This assumes that the basis are are orthonormal.)

Then it suffices to apply the matrix to the points in $A$.