What is the plot of "Charles" by Shirley Jackson?

The basic plot of Shirley Jackson's short story, "Charles," is as follows: 
Laurie is a boy who is beginning kindergarten. His mother is the narrator of this story. Laurie comes home with stories about what a boy in his class has done nearly every day. The boy's name is Charles. Charles hits the teacher, bangs the see-saw onto the head of a classmate, and throws chalk, among many other socially unacceptable deeds. 
Laurie's parents begin to wonder about the type of influence Charles is with their son. Laurie's father states that it's better for him to learn now rather than later how to deal with these things, because there are bound to be people like Charles in the world. 
All the while, Laurie is showing behaviors at home that mirror Charles's behavior. He yells loudly more than once, spills his baby sister's milk, and speaks insolently to his father. One example of this is when he says "Hi pop, y'old dust mop." 
For a short time, Laurie reports that Charles's behavior improves, but soon he is back to his old antics. He tells a girl to say an evil word in class, and she does. Then, Charles becomes bold enough to say the word himself. 
Laurie's mother attends the PTA meeting and is desperate to meet Charles's mother. Laurie's father asks his wife to invite Charles's mother over for tea so he can "get a look at her." Laurie's mother scans the faces of all the mothers during the PTA meeting to try to deduce which one is Charles's mother.  
Later, Laurie's mother approaches Laurie's teacher. Laurie's teacher remarks "We're all so interested in Laurie." She shares that Laurie had some trouble adjusting, but that he's a fine little helper now, "With occasional lapses, of course." Laurie's mother asks about Charles. The teacher replies that there is no student in kindergarten named Charles.  
 

Which symbols of atoms or ions are neutral?

The symbols for atoms are those found on the periodic table, such as H for hydrogen and He for helium. These symbols are assumed to represent the atom in its "ground state"—that is, the condition where it has an equal number of protons and electrons, and therefore a neutral charge. Therefore we can say that the symbol itself, by default, represents the atom in a neutral state. 
Ions, on the other hand, are by definition incapable of being neutral. An ion is an atom in a state where it has more or less than the ground state number of electrons. For example, an oxygen atom would normally have 8 protons and 8 electrons in its ground state, for a combined charge of 0. If the oxygen gained one extra electron, it would have a total charge of -1, and it would be considered an ion. If the oxygen lost an electron, it would have a charge of +1, and this would also be considered an ion. However, in neither state does the atom have any kind of overall neutral charge, so it cannot be represented that way. The representation for an ion is to show the symbol for the atom, with its overall charge in a superscript on the top right corner.
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/nucnot.html

How was Manifest Destiny represented visually?

Perhaps the most iconic visual representation of Manifest Destiny is John Gast's 1872 painting American Progress. It illustrates Manifest Destiny in the context of expansion into the western frontier. Columbia, a symbol long associated with the Americas, is depicted as a woman in a white dress leading the progressive path of western development. She carries a textbook and is trailing behind her a string of telegraph wire, followed by other symbols of western expansion and progress, such as the railroad.
We see other figures such as settlers and farmers moving westward with her, and there are other forms of transportation like the stagecoach and a horse-drawn wagon in the foreground. Scattering in the wake of this movement of "civilization" westward are a herd of buffalo, a bear, and a deer. These certainly symbolize the conquest and taming of nature. In this same light the painting features a group of apprehensive Native Americans fleeing the arrival of western settlers.
There are doubtless other depictions of Manifest Destiny. In the later nineteenth and early twentieth century one sees frequent caricatures of American imperial ambition in the form of newspaper cartoons, but few images are as iconic as American Progress.

Illustrate the differences between Henry and Victor's reactions on this trip in Chapter 19

Victor looks upon the trip, not as a nice vacation, but as more of a fact-finding mission. He wants to familiarise himself with the latest scientific developments in order to help him build the second monster. Victor, then, has a lot on his mind and so cannot enjoy the journey. In fact, it's a horrible experience for him as he's sunk deep in a dark depression. He's still emotionally torn between completing the second monster or destroying it altogether. And he remembers all too well the sinister threat made against him by the monster if he didn't build him a mate. Victor just wants to get the journey over with as soon as possible and get on with his work.
Henry, on the other hand, enjoys the trip immensely. But then again, he isn't burdened by a seemingly unsolvable moral dilemma. He sees the trip as a great opportunity to engage in learned conversation with men of genius and talent. Victor admits that he would've felt the same way as Henry in his happier days. Henry is, as Victor himself acknowledges, Frankenstein's former self, the eager, inquisitive young scientist bursting with curiosity about the world around him.
 

Calculus of a Single Variable, Chapter 9, 9.8, Section 9.8, Problem 10

sum_(n=0)^oo (2n)! x^(2n)/(n!)
To find radius of convergence of a series sum a_n , apply the Ratio Test.
L = lim_(n->oo) |a_(n+1)/a_n|
L=lim_(n->oo)| ((2(n+1))! x^(2(n+1))/((n+1)!))/((2n)! x^(2n)/(n!))|
L=lim_(n->oo) | ((2n+2)!)/((2n)!) * (x^(2n+2)/((n+1)!))/(x^(2n)/(n!))|
L=lim_(n->oo) | ((2n+2)!)/((2n)!) * x^(2n+2)/((n+1)!)*(n!)/x^(2n)|
L= lim_(n->oo) | ((2n+2)(2n+1)(2n)!)/((2n)!) * x^(2n+2)/((n+1)n!)*(n!)/x^(2n)|
L=lim_(n->oo) | ((2n+2)(2n+1)x^2)/(n+1)|
L=lim_(n->oo)|(2(n+1)(2n+1)x^2)/(n+1)|
L=lim_(n->oo) |(2(2n+1)x^2|
L=|2x^2|lim_(n->oo) |2n+1|
L=|2x^2| * oo
L=oo
Take note that in Ratio Test, the series diverges when L > 1.
So the series diverges except at x=0.
Since the series converges at x=0 only, therefore, the radius of convergence is R=0.

Modernism in movies has a greater impact than modernism in novels and other literature works. Argue this statement with valid explanations.

The Kite Runner is a good example of how modernism has a greater impact in film than it does in literature.  Modernism as an artistic movement rejects the “artificialities” of society, especially traditional European society, and embraces a more creative, permissive, amoral, and nihilistic process for creating artistic works, primarily in literature and film.  The movement is not characterized so much by what it embraces as by what it rejects: tradition, morality, religion, societal norms and class systems, convention, conformity, and the artistic standard of “mimesis, the literal imitation or representation of the appearance of nature, people and society.” (History of Modernism)
However, a film by its very nature can explore more avenues of creativity than a novel. The Kite Runner, for example, uses a personal narrative style to carry the story. Using nothing but words, the author shows his audience a very intimate look at another culture—not only the sights and smells of the cities but also the attitudes and, at times, dirty secrets of its citizens.  The film uses all this and more, using cinematography, music, sound effects, and visual effects to bring the story of Wazir Akbar Khan to life for the audience. People who would never have picked up the book flocked to the box office, giving the film a wider audience than the original novel. For those two reasons (wider variety in artistic form and style and access to a wider audience), it can be argued that modernism does have a greater impact both on the film industry and through the film industry than the average novel will ever be able to achieve.

In what way do Macbeth and Lord of the Flies compare in relation to power other than corruption?

In both William Golding’s Lord of the Flies and William Shakespeare’s Macbeth, the thematic idea of power is addressed. As your question states, most analysis of power in these texts focuses on the corruptive nature of power. However, both texts also present alternatives to this corruption through characters who are moral rulers.
Ralph in Lord of the Flies demonstrates the use of benevolent power. His natural leadership skills, and the fact that he blows the conch for the first time, cause the boys to select him as their chief despite Jack Merridew’s obvious experience as the choir leader. From the beginning, Ralph sets priorities for the boys and establishes rules to keep order on the island, such as the signal fire and building shelters.
Golding uses subtle descriptions to suggest Ralph’s temptation to be corrupted, such as his excitement upon landing a spear in the boar’s snout. Like Jack, Ralph is thrilled with the prospect of the violent hunt—an impulse that drives Jack to corruption in the novel. Despite these temptations, Ralph chooses the path of righteous leadership because he innately feels it is the best choice to serve the majority and achieve his goal of rescue. Although Jack represents absolute corruption, Ralph represents the moral leader who never allows his power to change his strength of character.
In Macbeth, Malcolm demonstrates his moral leadership. When he returns to the play in act IV, Malcolm has achieved several positive accomplishments in order to challenge the corrupt Macbeth. Malcolm has not only gotten the blessing of King Edward the Confessor but also amassed an army to join him in challenging Macbeth’s evil reign. Malcolm explicitly states his motivation for facing Macbeth when he tells Macduff he worries for the future of Scotland: “It weeps, it bleeds, and each new day a gash / Is added to her wounds” (4.3.41–42). This shows that Malcolm’s quest for power is actually a noble one. This is further demonstrated in Malcolm’s apprehension about killing Macbeth when he says that he is unsure of whether it is the right course of action, of which Macduff assures him. Malcolm’s triumph over Macbeth represents the triumph of good over evil, but it also shows that benevolent leaders who use their power for moral purposes will eventually prevail.
Ultimately, both Ralph and Malcolm represent a kind of power that diametrically opposes the corruption evident in Jack and Macbeth.