Given that B = curl A, use the divergence theorem to show that $\oint \mathbf{B} \cdot \mathbf{n} d \sigma$ over any closed surface is zero.

From the list at the top of the next page, identify the accounts that should be closed to Income Summary at the end of the fiscal year:

l. Wages Payable

Fill in the blanks with an appropriate word, phrase, or symbol(s). A closed figure in a plane determined by three of more straight line segments is called a(n) _.

Complete each sentence by filling in the blank with the correct term or person. 5. ______ were people who wanted land to be closed to the practice of slavery.

Prove that the divergence of a curl is always zero.

How many overtones are present within the audible range for a $2.44$-m-long organ pipe at $20\degree\mathrm{C}$
(a) if it is open, and (b) if it is closed?

In Fig. 22–13, how long does it take for the current, $I$, to reach its steady-state value after $S_1$ is closed?

Let A be a closed subspace of X. Show that if X is Lindelöf, then A is Lindelöf. Show by example that if X has a countable dense subset, A need not have a countable dense subset.

The gate shown is hinged at $H$. The gate is $3 \mathrm{~m}$ wide normal to the plane of the diagram. Calculate the force required at A to hold the gate closed.

Is it true that a discontinuous function cannot have both an absolute maximum and an absolute minimum value on a closed interval? Give reasons for your answer.

From the list at the top of the next page, identify the accounts that should be closed to Income Summary at the end of the fiscal year:

j. Supplies Expense

Find the absolute maximum and minimum values of $f ( x ) = x - \tan x$ in the closed interval [ - \pi / 4 , \pi / 4 ] , and state where those values occur.

From the following list, identify the accounts that should be closed to Income Summary at the end of the fiscal year under a perpetual inventory system: (f) Supplies

Indicate whether the following statements are true or false. Explain. If a closed system undergoes a thermodynamic cycle, there can be no net work or heat transfer.