Use the basic definition of a Cartesian tensor to show the following. (a) That for any general, but fixed, ϕ, (u1, u2)=(x1 cosϕ-x2 sinϕ, x1 sinϕ x2 cosϕ) are the components of a first-order tensor in two dimensions. (b) That ( x2^2 x1 x2 x1 x2 x1^2) is not a tensor of order 2. To establish that a single element does not transform correctly is sufficient. | Numerade
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