1Cademy - Consider the transformation applied to a 2-dimensional vector $\mathbf{x} = [x_1, x_2]$ by an angle $\theta$, defined by the formula: <br><br>$\mathrm{Result} = [\cos(\theta) \cdot x_1 - \sin(\theta) \cdot x_2, \sin(\theta) \cdot x_1 + \cos(\theta) \cdot x_2]$<br><br>This transformation alters the magnitude (length) of the vector $\mathbf{x}$.

True/False

Consider the transformation applied to a 2-dimensional vector $\mathbf{x} = [x_1, x_2]$ by an angle $\theta$ , defined by the formula:

$\mathrm{Result} = [\cos(\theta) \cdot x_1 - \sin(\theta) \cdot x_2, \sin(\theta) \cdot x_1 + \cos(\theta) \cdot x_2]$

This transformation alters the magnitude (length) of the vector $\mathbf{x}$ .

Updated 2025-10-09

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