Draw one line under each main clause and two lines under each subordinate clause. Write C in the blank if the sentence is complex and CC if it is compound-complex. _____ Because Todd stays up so late, he keeps the rest of us from sleeping, and we are getting tired of it.

Assuming an operating frequency of $1 \text{ kHz}$, transform the following phasor expressions into a single cosine function in the time domain: (a) $9\angle 65^{\circ}\;\mathrm{V}$. (b) $\dfrac{2\angle 31^{\circ}}{4\angle 25^{\circ}}\;\mathrm{ A}$. (c) $22\angle 14^{\circ}- 8\angle 33^{\circ}\;\mathrm{V}$.

Explain the meaning of the given statement, which contains a multiple negation. Then answer the question that follows.
Sarah did not decline the offer to go to dinner. Did Sarah go to dinner?

For each of the following sentences, identify the underlined clause as an adjective or an adverb. Above each, write $A D J$ for adjective or $A D V$ for adverb. Then, circle the word the clause modifies $\underline{After we wash these shells}$, we can glue them to the poster board.

Propan-1-ol is freely soluble in water, butan-1-ol is marginally soluble, and hexan-1-ol is essentially insoluble. Explain.

A 25-kg ladder of length 5.0 m leans against a smooth wall and makes an angle of $50 ^ { \circ }$ with the ground. A 75-kg man starts to climb the ladder. If the coefficient of static friction between ground and ladder is 0.50, what distance along the ladder can the man climb before the ladder starts to slip?

Let $C$ be a piecewise-smooth Jordan curve that does not pass through the origin. Evaluate

$$\oint_C-\frac{y^3}{\left(x^2+y^2\right)^2} d x+\frac{x y^2}{\left(x^2+y^2\right)^2} d y$$

a. if $C$ does not enclose the origin. b. if $C$ does enclose the origin.

Add an adverb clause to each sentence, in the place indicated by a caret. Begin the clause with the subordinating conjunction shown in parentheses. Usage Tip: An adverb clause must contain both a subject and a verb. Example: Original $~$ She felt at home walking by herself through the woods, (even though) Rewritten Even though Sylvia was easily frightened, she felt at home walking by herself through the woods.

^ She finds the cow near the swamp. (after)

Solve the equation. Check your solution, if possible.

It is given that $\angle A B C \cong \angle C B D$. A student concludes that because $\angle A B C$ and $\angle C B D$ are congruent adjacent angles, $\overleftrightarrow{A B} \perp \overleftrightarrow{C B}$. What is wrong with this reasoning? Draw a diagram to support your answer.

The slender bar is released from rest with $\theta=45^{\circ}$ and falls a distance $h=1 \mathrm{~m}$ onto the smooth floor. The length of the bar is $1 \mathrm{~m}$ and its mass is $2 \mathrm{~kg}$. If the coefficient of restitution of the impact is $e=0.4$, what is the angular velocity of the bar just after it hits the floor?

For each case, identify the force (including its direction) that causes the acceleration.

$(b)$ Ahockey puck skidding freely but slowly coming to rest on the ice.

Answer the following questions:

• a. What is a financial responsibility law?
• b. What is a compulsory insurance law?

Show that the cross product is not associative by finding vectors $\vec{x}, \vec{y}$, and $\vec{z}$ such that $(\vec{x} \times \vec{y}) \times \vec{z} \neq \vec{x} \times(\vec{y} \times \vec{z})$.