The emperor used falsified news stories to _____ the public into believing in fictional enemies, while his Department of Information enshrouded the population in ignorance by cutting off all Internet access to the world beyond their borders. A. delude B. obtrude C. dally D. cogitate E. broach.

Faced with a difficult life decision, the pensive student left the noise of town to be alone on the mountain, where he could ______ in quiet solitude and arrive at a solution to his problem. A. dally B. alienate C. cogitate D. knead E. amalgamate.

A scientific breakthrough caused a[n] ______ in the company's antiquated methods of production. A. renaissance B. gorge C. insurrection D. prose E. numismatist.

During the international _____ to discuss nuclear waste, representatives of several nations deliberated over the facts. A. opiate B. edifice C. forum D. renaissance E. caricature.

Solve the given differential equation. $x^{2} y^{\prime \prime}+3 x y^{\prime}-4 y=0$

Two aqueous sulfuric acid solutions containing 20.0 wt% $\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{SG}=1.139)$ and 60.0 wt% $\mathrm{H}_{2} \mathrm{SO}_{4}$ (SG = 1.498) are mixed to form a 4.00 molar solution (SG = 1.213). a) Calculate the mass fraction of sulfuric acid in the product solution. b) Taking 100 kg of the 20% feed solution as a basis, draw and label a flowchart of this process, labeling both masses and volumes, and do the degree-of-freedom analysis. Calculate the feed ratio (liters 20% solution/liter 60% solution). c) What feed rate of the 60% solution (L/h) would be required to produce 1250 kg/h of the product?

People respond to incentives because

a. incentives act as rewards that encourage people to behave in certain ways.

b. incentives exploit opportunities to make people better off.

c. incentives exploit opportunities to make people worse off.

d. incentives discourage the use of free time.

Some of the vocabulary words have related meanings. Complete the following sentence by choosing the word that best fits the context, based on information you infer from the use of the italicized word. Some word pairs will be antonyms, some will be synonyms, and some will simply be words often used in the same context.

The sight of a rat running through the restaurant's dining room on live television was an imbroglio that ____________ customers and the eatery for years after the event.

A. comprised

B. estranged

C. contrived

D. revered

E. venerated

The author's funny ______ was delightful to read, especially in the way it portrayed the eccentric townsfolk as hilarious caricatures of their real-life counterparts. A. paucity B. forum C. opiate D. prose E. thesis.

Complete the following sentences by choosing the word that best fits the context, based on information you infer from the use of the italicized word. Some word pairs will be antonyms, some will be synonyms, and some will simply be words often used in the same context. The prodigal student received light punishments for his pranks at school, but when he tried to pull the same pranks as an adult at his job, he was labeled a[n] ____ and promptly fired. A. renegade, B. retribution, C. exodus, D. uncanny, E. plebeian.

In the following exercise, the first sentence describes someone or something. Infer information from the first sentence, and then choose the word from the Word Bank that best completes the second sentence. Egalitarian, chauvinist, paucity, antiquated, beleaguer, felonious, gall, ambidextrous. Mort complained about changes to the club rules until they proved to be wildly successful, and then he took full credit for the changes. From this sentence, we can infer that Mori has a lot of ______ f or taking credit for things he didn't do.

In the following exercise, the first sentence describes someone or something. Infer information from the first sentence, and then choose the word from the Word Bank that best completes the second sentence. Egalitarian, chauvinist, paucity, antiquated, beleaguer, felonious, gall, ambidextrous. The major league batter could hit right-handed as well as he could hit left-handed, which made it difficult for pitchers to adapt to him. From this sentence, we can infer that the batter is _____.

2. $81 \div 3 =$

Let $A$ be an $m \times n$ matrix, $B$ an $n\times r$ matrix, and $C = AB$. Show that a. $Null(B)$ is a subspace of $Null(C).$ b. $Null(C)^{\perp}$ is a subspace of $Null(B)^{\perp}$ and, consequently, $Col(CT)$ is a subspace of $Col(BT )$.