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a). Find a linear map of the plane, $A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that does the following transformation of the letter $\mathbf{F}$ (here the smaller $\mathbf{F}$ is transformed to the larger one):

b). Find a linear map of the plane that inverts this map, that is, it maps the larger $\mathbf{F}$ to the smaller.

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