Find the basis of vectors for the set S = {(1, -2, 3), (-2, 4, -6), (3, -6, 9)}.
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What is the smallest value of n that satisfies Fermat's Theorem, where a^n + b^n = c^n for a, b, c > 0, and n > 2? (Hint: The answer might surprise you!)
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What is the derivative of f(g(x)) using the Chain Rule, if f(x) = sin^2(x) and g(x) = x^3 - 1?