A two-dimensional vector is represented as x = [3, 4]. Calculate the resulting vector after applying a rotational transformation with an angle θ = 90° (π/2 radians).

Consider the transformation applied to a two-dimensional vector $x = \begin{bmatrix} x_1 & x_2 \end{bmatrix}$ by an angle $\theta$, resulting in a new vector $y = \begin{bmatrix} \cos \theta \cdot x_1 - \sin \theta \cdot x_2 & \sin \theta \cdot x_1 + \cos \theta \cdot x_2 \end{bmatrix}$. This transformation will always alter the magnitude (or length) of the original vector $x$.

Analysis of Rotational Transformation Properties