Determine whether the vectors v and w are orthogonal.v = 3i - 6j, w = -6i + 3j
A. Orthogonal
B. Not orthogonal
Answer: B
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Find the gradient field F of the function f.f(x, y, z) = 
A. F = - 
i - 
j - 
k
B. F = - 
i - 
j - 
k
C. F = 
i + 
j + 
k
D. F = 
i + 
j + 
k
Evaluate the definite integral. Express the answer in terms of natural logarithms.
A. ln(8 + 
)
B. ln 9
C. ln(
)
D. ln(8 + 3
)
Solve the problem.A stone is thrown into a pond. A circular ripple is spreading over the pond in such a way that the radius is increasing at the rate of 2.6 feet per second. Find a function, r(t), for the radius in terms of t. Find a function, A(r), for the area of the ripple in terms of r. 
A. (A ? r)(t) = 6.76?2t B. (A ? r)(t) = 2.6?t2 C. (A ? r)(t) = 5.2?t2 D. (A ? r)(t) = 6.76?t2
Answer the question.How can the graph of f(x) = 
- 11 be obtained from the graph of 
A. Reflect it across the y-axis. Shift it 11 units down. B. Reflect it across the x-axis. Shift it 11 units down. C. Reflect it across the x-axis. Shift it 11 units up. D. Reflect it across the y-axis. Shift it 11 units up.