The vector \( [5,\ 3] \) in a right-handed planar coordinate system was transformed to a different coordinate system resulting in the vector \( [6.66,\ 12.20] \) using a four-parameter similarity transformation.
Select the CORRECT set of transformation parameters from the choices given below. The transformation parameters are given in the following order: scale, rotation angle, translation vector.
Hint: For a right-handed system, the rotation matrix \( R(\theta) \) in two dimensions is given as
\[ R(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}. \]