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Find the angle between the given vectors.u = i – j, v = 3i + 5j Round to the nearest tenth of a degree.

Find the domain of the vector-valued function.

Solve the initial value problem.Differential Equation:  = (sec2t)i + (4t3- 3)jInitial Condition: r(0) = -6j

Find the Jacobian J(u, v). u = 5x – 3y,      v = -3x + 5y

Use the given transformation to evaluate the integral.

Solve the problem.Let R ={(x, y): 1 ≤ x < 4, 0 ≤ y < 4}. Evaluate  

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.The curve y = ln x and the lines x = 8 and y = 0

Find the transformation from the uv-plane to the xy-plane.,    

Solve the problem.Let R ={(x, y): 1 ≤ x < 5, 0 ≤ y < 7}. Evaluate

Find the average value of F(x, y, z) over the given region.F(x, y, z) = xyz over the rectangular solid in the first octant bounded by the coordinate planes and the planes x = 6, y = 4, z = 3.