R^2/Ellipse to itself/No rotation/Exercise

Give an example of a (symmetric to the axes) ellipse ${}E$ in ${}\mathbb {R} ^{2}$ and a bijective linear mapping ${}\varphi \colon \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$ with ${}\varphi (E)=E$ that is not an isometry.

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