Question
Define covariant and contravariant tensors of rank two. Show that the velocity and acceleration are contravariant vectors.
Answer :
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A tensor of rank two is an array of components that transform in a specific way under a change of coordinates. A covariant tensor of rank two (T_{ij}) has components that transform according to the rule: [ T'*{kl} = \frac{\partial x^i}{\partial x'^k} \frac{\partial x^j}{\partial x'^l} T*{ij} ] where (x^i) are the original coordinates and (x'^k) are the transformed coordinates. Covariant tensors transform with the derivatives of the old coordinates with respect to
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