`u = ` Use the dot product to find the magnitude of u.

The magnitude of a vector `u` is the square root of its product by itself, because

`u*u=||u||*||u||*cos(theta),`

and `theta=0,` `cos(theta)=1.` So

`||u||=sqrt(u*u)=sqrt(lt-8,15gt*lt-8,15gt)=` `=sqrt((-8)*(-8)+15*15)=sqrt(64+225)=sqrt(289)=17.`

This is the answer.

The magnitude of a vector `u` is the square root of its product by itself, because

`u*u=||u||*||u||*cos(theta),`

and `theta=0,` `cos(theta)=1.` So

`||u||=sqrt(u*u)=sqrt(lt-8,15gt*lt-8,15gt)=`
`=sqrt((-8)*(-8)+15*15)=sqrt(64+225)=sqrt(289)=17.`

This is the answer.

Valence Bond Theory fails to explain the paramagnetic character of the oxygen molecule. Why is this?

Valence bond theory predicts that all electrons in diatomic oxygen are spin paired, making O2 diamagnetic.  However, we know that diatomic oxygen is paramagnetic.  This means that electrons are not spin paired.  

If we apply valence bond theory, each oxygen in O2 looks like this:

2p  _e-/e-_  _e-_  _e-_  (remember that electrons, when paired, spin in opposite directions and are drawn as arrows pointing up/down)

2s  _e-/e-_

1s  _e-/e-  (usually not shown because only...

Valence bond theory predicts that all electrons in diatomic oxygen are spin paired, making O2 diamagnetic.  However, we know that diatomic oxygen is paramagnetic.  This means that electrons are not spin paired.  

If we apply valence bond theory, each oxygen in O2 looks like this:

2p  _e-/e-_  _e-_  _e-_  (remember that electrons, when paired, spin in opposite directions and are drawn as arrows pointing up/down)

2s  _e-/e-_

1s  _e-/e-  (usually not shown because only valence electrons are considered)

This is because oxygen has the atomic number 8 and therefore has 6 valence electrons (the other 2 are in the first shell of the atom).  The 1s shell represents this first shell.  The second shell includes one "s" and 3 "p" orbitals.  The s orbitals must be filled with spin paired electrons first and then the ones that are left over are used to fill the 3 p orbitals.  We start by putting one electron in each of the p orbitals.  This uses three of the four electrons that we still have to place.  The last one becomes spin paired with the electron in the first p orbital to fill that orbital.  The other two p orbitals contain unpaired electrons.  

Using valence bond theory, you would predict that because each oxygen has those 2 unpaired electrons in their p orbitals, the two oxygens would form a covalent (double) bond and each would share their two unpaired electrons to fill their p orbitals leaving no unpaired electrons and making O2 diamagnetic.  This isn't the case, of course.  

O2 is paramagnetic with unpaired electrons.  One must apply molecular orbital theory to understand why.  This goes a step beyond valence bond theory.

We know that with O2 we have four total electrons in the "2s" orbitals (2 from each oxygen).  These electrons are going to form something called sigma bonds.  When you diagram molecular orbitals, there are both bonding and antibonding orbitals that must be drawn.  These 4 "2s" electrons are going to be split into 1 bonding sigma orbital (2 electrons) and 1 antibonding sigma orbital (2 electrons).  

We then move on to the "2p" orbitals.  Each oxygen has 4 "2p" electrons.  These electrons are going to go into sigma and pi bonds.  When you diagram this, you have two pi bonding orbitals and one sigma bonding orbital and then corresponding higher energy (filled after low energy bonding orbitals) pi (2) antibonding orbitals and one antibonding sigma orbital.  

Again, you use the "2p" electrons from both oxygens to fill these molecular orbitals.  You start out by using 4 of the 8 "2p" electrons to fill the two bonding pi orbitals and then 2 more to fill the one bonding sigma orbital.  This leaves 2 electrons.  They are added to the higher energy antibonding pi orbitals (you'll see them as pi star).  

One electron is added to each pi orbital so there are 2, unpaired electrons in the antibonding pi orbitals.  This is where the paramagnetic behavior of O2 comes from.  Whereas valence bonding theory predicts that all electrons will be paired, using the molecular orbital theory, you can see that there are unpaired electrons making O2 paramagnetic.

How does Mrs. Mallard's heart condition impact the way other characters interact with her?

The characters with whom we see Mrs. Mallard interact in the story are her sister and her husband's friend Richards.  We also are privy to Mrs. Mallard's thoughts about her relationship with her husband. With all three characters, there is evidence to show that Mrs. Mallard's heart condition has caused those around her to treat her far more carefully than a woman of normal health.

The very first sentence of the story tells us,

Knowing that Mrs. Mallard was afflicted with a heart trouble, great care was taken to break to her as gently as possible the news of her husband's death (para. 1). 

This sets the stage for Mrs. Mallard's interactions with those around her.

Mrs. Mallard's sister, Josephine, finds it necessary to be indirect in breaking the news of Mr. Mallard's death, "in veiled hints..." (para. 2). And when Mrs. Mallard retreats to her room and closes her door, Josephine kneels in front of the door begging Mrs. Mallard to open the door, telling her she will make herself sick.

Mr. Mallard's friend Richards checks twice to be sure that Mr. Mallard is on the fatality list.  Then he hurries to the house to be sure that he can break the news before someone less sensitive to Mrs. Mallard's delicate state could let her know in a way that would be less tender and careful. 

While we do not see Mr. and Mrs. Mallard together in the story, except for that one fleeting moment at the end, there is evidence to suggest that Mr. Mallard might have been controlling and dominating to some degree because of his wife's heart condition.  She thinks of his "powerful will bending hers..." (para. 12) with "kind intention...." (para. 12).  We can speculate that at the very least, this was his justification for being a controlling spouse. 

The way this story is set up, it makes sense for Mrs. Mallard to have a heart condition, so it is plausible that she dies from shock, and the interactions with others are meant to show this.  But I don't think it is a coincidence that she has a heart condition.  This is almost a play on words, really, since the condition Mrs. Mallard suffers from is certainly a condition of the heart, an inability to be her own person in her marriage. 

In The House on Mango Street, what are the folks in the chapter "And Some More" doing or talking about?

 In the chapter "And Some More" of Sandra Cisneros' The House on Mango Street, Esperanza and her sister Nenny are having a conversation with their neighbor girls, Rachel and Lucy. The conversation begins with Esperanza trying to show off a little bit by mentioning that she read in a book about how the Eskimos have thirty different names for snow. The conversation is quickly distracted from names for snow to talking about names for a variety of things.

Esperanza seems to be talking about the concept of naming things based on different characteristics they have. Her initial comment about the thirty names for snow implies that those names all have slightly different meanings or at least bring our attention to different qualities of the snow. The same is true of the names for clouds, cumulus and nimbus being specific types of cloud formations. 

This is contrasted with the comments of the other three girls, who are merely naming things for the sake of calling them something. Nenny spends the majority of the chapter simply listing different human names and attributing them to various clouds she sees in the sky. 

Lucy is mostly just chattering in a mindless but insulting sort of way, and says rather off-handedly that Esperanza's mama is ugly. Esperanza becomes very offended by this, and starts to escalate the conversation into an argument in an effort to make the other girls see what they've said. The chapter ends with saying that all four girls are stupid.

This chapter underscores the vast difference between the childish behavior of Nenny, Lucy and Rachel, and the very serious mind that Esperanza has. She interprets a casual and silly comment as a severe insult and is sufficiently wounded by it to choose not to be friends with Lucy and Rachel anymore.

Can you summarize the entire book From Reverence to Rape?

From Reverence to Rape: The Treatment of Women in the Movies is a book written by film critic Molly Haskell. It was first published in 1974, and a second edition with a chapter covering films released from 1974-1987 was published more recently. The book is mainly divided into chapters covering a entire decade of film, with chapters on The Twenties, The Thirties, and so on, with chapters also on "The Woman's Film" and "The Europeans."...

From Reverence to Rape: The Treatment of Women in the Movies is a book written by film critic Molly Haskell. It was first published in 1974, and a second edition with a chapter covering films released from 1974-1987 was published more recently. The book is mainly divided into chapters covering a entire decade of film, with chapters on The Twenties, The Thirties, and so on, with chapters also on "The Woman's Film" and "The Europeans." Haskell was a film critic for The Village Voice and later New York Magazine and Vogue. One of the main points made in the book is that despite many inroads made in women's lives, cinema in the 1970s portrayed women in increasingly negative ways, as prostitutes, victims or weaklings, for example. Haskell informs her critique with feminist theory, and reviews of the book often note the angry and bitter tone of her analysis. She considers it a terrible irony that women's equality has not been adequately represented in movies:

"Here we are today, with an unparalleled freedom of expression, and a record number of women performing, achieving, choosing to fulfill themselves, and we are insulted with the worst--the most abused, neglected, and dehumanized--screen heroines in film history."

The book was considered very groundbreaking at the time, and is still considered an important text in the scholarly fields of film studies and women's studies.

In Of Mice and Men, how can the question Carlson asks at the very end of the story be answered?

In John Steinbeck's novella Of Mice and Men characters such as George, Slim, Crooks and Candy are portrayed as men of heightened sensibilities. They know that the world is not always a "black and white" place. They tend to understand that the world is a complicated place, often without clear moral conclusions.

At the end of the novel George is virtually forced into the mercy killing of his best friend Lennie, after the mentally challenged...

In John Steinbeck's novella Of Mice and Men characters such as George, Slim, Crooks and Candy are portrayed as men of heightened sensibilities. They know that the world is not always a "black and white" place. They tend to understand that the world is a complicated place, often without clear moral conclusions.

At the end of the novel George is virtually forced into the mercy killing of his best friend Lennie, after the mentally challenged man inadvertently kills Curley's wife. After performing the heartbreaking deed George is consoled by Slim, the leader of the working men on the ranch which is the setting of the book. Slim says, “You hadda, George. I swear you hadda. Come on with me.”

Slim's words are small consolation, but for George they let him know that at least one person realizes his love for Lennie and how he protected him and kept him free from abuse. If George had not killed Lennie the big man may have fallen prey to the brutality of Curley or the anonymous apathy of the legal system. At any rate, Lennie would not have understood what was happening to him if he had been captured. He only understood that he had done "another bad thing" and that George was going to "give him hell."

Unlike Slim, Carlson does not understand George's actions and in the very last lines of the novel he says, “Now what the hell ya suppose is eatin’ them two guys?” Earlier in the book Carlson shoots Candy's dog in what he calls an act of mercy, but in reality Carlson kills the dog because the dog is an irritant to him. Consequently, he does not understand that George has killed his friend for the very same reason that the old dog needed to be put down. 

Earlier in the book Candy confesses to George:

“I ought to of shot that dog myself, George. I shouldn’t ought to of let no stranger shoot my dog.”

George obviously took those words to heart and he denies Curley or Carlson the chance to kill Lennie. Both Curley and Carlson are static characters who cannot fathom the depth of affection which both George and Candy felt for their friends.

Was slavery the primary cause of the Civil War? Explain. In any scenario could the Civil War have been avoided?

Slavery per se was not the primary cause for the Civil War; economic reasons were the primary causes. But, slavery certainly played a large part of the Southern economy.

The development of an agrarian economy in the South that was dependent upon slavery and the expansion of an industrial economy in the North that was based on free labor set up the incompatibility of these economies that led to the conflicts which effected the War Between the States. 

Among these conflicts were sectional conflicts over territories in the West which both sections of the country saw as necessary to their continued development: the North needed more areas for the growth of food as its populations grew; the South desired more land for its agrarian economy. There was also the "foot-race between the competing labor systems"; that is, the creation of new slave or free states. This became a contentious issue, for if the states of one labor system (free vs. slave) became larger in number than the other's, the Congress of the United States could pass laws abolishing the system of labor of the smaller block of states.

The North was becoming more and more unwilling to allow the South to expand slavery as there were many who objected to it on moral grounds and others who did not want the West to become slave states for political reasons. Added to this issue, there was the issue of tariffs. Because the North wanted their industries to prosper, it imposed tariffs on products coming into the country. Since the South needed many of the products made by industries of the North or other places, it had to pay tariffs. Therefore, the South tried to stop tariff increases. 

Compromise with the South became less and less likely with the North because of the moral, political and economic issues of slavery and the economic issue of tariffs. In 1854 this Northern opposition led to the formation of the Republican Party, which then supported the interests of the North [Encyclopedia. com]. When Abraham Lincoln was a candidate for president, he supported entirely the economic interests of the North; so, when he became president, the South felt it had no choice but to secede from the Union if it wished to preserve its economic system, a system that included slave labor.

While there are a number of viewpoints on the Civil War, one viewpoint is that this war could have been avoided if Lincoln had allowed to South to secede, an act which was constitutional according to Jeffersonian democracy:

This was a right that continued throughout the initial drafts of the Articles of Confederation, the Constitution and the Declaration of Independence.

But, instead, President Lincoln ordered the military blockade of the ports that belonged to the South, which was actually an act of war.