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Show that in 2D, the general orthogonal transformation as matrix A given by {{cos, sin}, {-sin, cos}}. Verify...

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Physics

Showthat in 2D, the general orthogonal transformation as matrix A givenby
{{cos, sin}, {-sin, cos}}. Verify that det[A] = 1 and that thetranspose of A equals its inverse. Let Tij be a tensor in thisspace. Write down in full the transformation equations for all itscomponents and deduce that Tii is an invariant.

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