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I haven't studied multivariable calculus yet but I have a question that bothers me. Let $F$ be a function $R^{2} \to \ R$ .Imagine that we rotate the co-ordinate axis by an angle $\theta$ .Then I think the shape of the function should change.How should this function change if we make a rotation of the co-ordinate axis by some angle?

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Do you mean to rotate in the plane of inputs $R^2$? If so this will only rotate the entire graph of $F$. If you want to rotate the entire $R^3$ in which the graph lies, the rotation may not even give the graph of a function. –  coffeemath Nov 4 '12 at 23:04
Yes, I mean to rotate the domain . How can we express the new function in terms of the old function and the angle $\theta$? –  Nabil Nov 5 '12 at 8:45

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