A transformation is applied to a d-dimensional vector $\mathbf{x}$ at position $t$ using a set of frequencies $\theta$. The full transformation is defined by the following element-wise formula: $\mathrm{Trans}_{full}(\mathbf{x}, t\theta) = \begin{pmatrix} x_1 x_2 \vdots x_{d-1} x_d \end{pmatrix} \odot \begin{pmatrix} \cos t\theta_1 \cos t\theta_1 \vdots \cos t\theta_{d/2} \cos t\theta_{d/2} \end{pmatrix} + \begin{pmatrix} -x_2 x_1 \vdots -x_d x_{d-1} \end{pmatrix} \odot \begin{pmatrix} \sin t\theta_1 \sin t\theta_1 \vdots \sin t\theta_{d/2} \sin t\theta_{d/2} \end{pmatrix}$ Now, consider a simplified version of this transformation where the second term (involving the sine vector) is removed: $\mathrm{Trans}_{simple}(\mathbf{x}, t\theta) = \begin{pmatrix} x_1 x_2 \vdots x_{d-1} x_d \end{pmatrix} \odot \begin{pmatrix} \cos t\theta_1 \cos t\theta_1 \vdots \cos t\theta_{d/2} \cos t\theta_{d/2} \end{pmatrix}$ Analyze the effect of this simplification. What geometric property of the full transformation is lost in the simple version, and what operation does the simple version perform instead?