Application of RoPE Rotation to a 2D Vector

Definition of the 2x2 RoPE Rotation Matrix Block

A developer is implementing a function to rotate a 2D row vector v counter-clockwise by an angle θ. The operation is performed by post-multiplying the vector by a 2x2 matrix R (i.e., v_rotated = vR). Which of the following matrices correctly represents this transformation?

Constructing a 90-Degree Rotation Matrix

Consider a transformation applied to a 2D row vector v by post-multiplying it with a matrix R (i.e., v_rotated = vR). The matrix $R = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ correctly performs a counter-clockwise rotation of the vector by an angle θ.