Employ these relations to determine (E) and (): av

Calculate with residual theorem application dx Jo (x²+1)(x²+4)²

Conslder the following. TIs the counterdockwise rotation of 45° in R, v = (2, 2). %3D (a) Find the standard matrix A for the linear transformation 7. (b) Use A to find the image of the vector v. 7(v) (c) Sketch the graph of v and its image. y. T(V)

Prove the formula?

can you plz solve (d) (e) (f)?

without a calculator ，please solve for x by hand. Need to show every step！

(3) The natural independent variables for U are (S, V), from dU = TdS – pdV. U = U(S,V) (), instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely gives simple expressions for T and p as T = and ().: Suppose you use (V,T) p = - V dT + f(V), %D T where f (V) is an unknown function of V.