Geometry, Quaternions, Rotations

Question

For a coordinate system $C_2$, if I have the angles made by its coordinate axes ($x_2$,$y_2$ and $z_2$) with the coordinate axes($x_1$, $y_1$ and $z_1$) respectively of another coordinate system $C_1$, how do I find the rotation matrix or the rotation quaternion required to move from the coordinate system $C_1$ to $ C_2$.