How can the title of the story "The Canterville Ghost" be justified?

I believe that the question is asking why this story is called "The Canterville Ghost" instead of having some other title. I understand the question, and it is a good question because the title of the story could absolutely be focused on the Otis family. The title could have been something like "The Otis Haunting."

"The Canterville Ghost" as a title makes the most sense to me because Sir Simon's ghost is the most interesting character in the story. The Otis family is hilarious, but ultimately the Otises are flat characters. They are the same throughout the story, and that is also true of Virginia Otis. Having the title focus on the Canterville ghost helps focus the reader's attention on that character. Sir Simon is by far the most interesting and dynamic character in the story because readers get to see a wide range of his emotions. We see him exuberant and overconfident in his abilities to scare off new homeowners. We see him angry at the Otis family and even scared of the Otis family. By the end of the story, most readers will even sympathize with Sir Simon's situation. The title, "The Canterville Ghost," is an effective title because it is a short, to-the-point title that correctly focuses reader attention on the most important character.

What were some immediate effects and long term effects of the Protestant Reformation?

The immediate effect of the Protestant Reformation is that it led to a schism that culminated in the creation of several new denominations within western Christianity. The teachings of Martin Luther and others were reflected in the establishment of new churches throughout Western Europe in locations like Germany and Switzerland. This meant that the Catholic Church lost a great deal of political power, especially in the collection of principalities and city-states known as the Holy Roman Empire, and of course in England, where Henry VIII formally separated the kingdom from the Church in 1534.

Some of the long-term effects of the Reformation included the outbreak of religious wars in the Holy Roman Empire and France that spanned much of the sixteenth and seventeenth centuries. These included the Thirty Years' War, which devastated the region. But the Reformation, because Protestants emphasized the primacy of Scriptural authority, also fostered literacy in Western Europe. Above all, it led to the flowering of dozens of Protestant sects that changed modern Christianity forever. 

Solve cos^2(x)=sin(x)

First we must get everything in the same terms. Here I'll choose sin(X) because it is the easiest. So we need to use a trig identity to substitute for `cos^2(X).`

`Cos^2(X)=sin(X)`

`1-sin^2(X)=sin(X)`

Then we can treat this like a quadratic equation. So we will move all the terms to one side and have our equation equal to 0.

`1-sin^2(X)-sin(X)=0`

Now we can rearrange the equation so that it is in standard quadratic equation form. But instead of having the equation in terms of X, we have an equation in terms of sin(X).

`-sin^2(X)-sin(X)+1=0`

`-1(sin(X))^2-1(sin(X))+1=0`

Next, just as we could solve for x in a quadratic equation, we can solve for sin(X) in this equation using the quadratic formula.  

`sin(X)=(+1+-sqrt((-1)^2-4(-1)(1)))/(2(-1))`

`sin(X)=(1+-sqrt(5))/-2`

`sin(X)~~-1.618 or 0.618`

As usual with the quadratic formula, we have two possible values.  We will then need to find the degree measure X by finding the arcsine of the values we found above.  But because sine values must fall between -1 and 1, we can throw out -1.618 as a possible value. Thus we only need to use the value 0.618 as our sine value.

`sin(X)~~0.618`

`X~~sin^-1(0.618)`

`X~~38.17^o`  

 Note that this is not the only degree measure that will give this sign value. There is also a degree measure in Quadrant II that will have the same sine value. We can find that value like so:

`X~~180-38.17=141.83^o`

There are also infinitely many other degree measures that will have this sign value. Every time you move around the unit circle and come upon these degree measures in Quadrants I and II, the sine value will be the same. So all possible values of X are:

`X~~38.17+-360n and X~~141.83+-360n`

In 1984, how does the Party control the minds of its citizens?

In 1984, the Party controls the minds of its citizens in two ways. The first of these is through propaganda: it controls of the flow and content of information and erases any aspects which portray it in an unfavourable light. We see this in Part One, Chapter Four, for instance, when Winston erases a "pledge" made by the Party stating that the chocolate ration would not be reduced. In its place, he writes that the ration will have to be reduced "sometime in April" in preparation for a forthcoming reduction from "thirty grammes to twenty."

Additionally, the Party uses violence to control the minds of its citizens. This job is carried out by the Thought Police who imprison thought criminals (people who criticise the Party) in the Ministry of Truth. From Winston's experience in Part Three, we see that the Party uses torture and Room 101 to make people believe what it tells them and, ultimately, to "love Big Brother."

Although diverse in their treatment and technique, many stories are about individuals struggling with a complex sets of external forces that...

In Tan's "Two Kinds" and Jackson's "The Lottery," social expectation regulates in self-definition.

Social expectation plays a large role in forming June's identity and in guiding Suyan's hopes for her daughter. Suyuan believes that her daughter can be a child prodigy because, in America, "you could be anything you wanted to be." This mythology is associated with the dream of unlimited hope in America. Aspiring to this standard causes her to embrace a "Shirley Temple" prodigy image for her daughter. At first, June also embraces this external reality in the way she sees herself:

In fact, in the beginning I was just as excited as my mother, maybe even more so. I pictured this prodigy part of me as many different images, and I tried each one on for size. I was a dainty ballerina girl standing by the curtain, waiting to hear the music that would send me floating on my tiptoes. I was like the Christ child lifted out of the straw manger, crying with holy indignity. I was Cinderella stepping from her pumpkin carriage with sparkly cartoon music filling the air.

June and Suyan form their definition of identity in accordance to an external reality. Eventually, June rejects this definition. The hurt this triggers between mother and daughter reflects the zeal with which both allowed something external to influence both of their identities. The social expectation of how people in America are supposed to act regulates June's self-definition, and her mother's hopes for her.

In Jackson's "The Lottery," self-definition is seen in the social expectation of the lottery. The town's tradition defines how people see themselves. Old Man Warner articulates the social importance of the town's ritual:

Pack of crazy fools [people who want to get rid of the lottery]...  Listening to the young folks, nothing’s good enough for them. Next thing you know, they’ll be wanting to go back to living in caves, nobody work any more, live that way for a while. Used to be a saying about Lottery in June, corn be heavy soon... There’s always been a lottery...

The lottery is an embedded part of cultural practice and individual identity. It regulates the way people in the town see themselves. Old Man Warner's beliefs link the lottery to agricultural bounty, social advancement, and cultural practice.

Jackson shows how the people in the town view their own identity in accordance to the lottery. For example, Tessie Hutchinson looked forward to the lottery. She was excited and eager to attend the proceedings. At the story's start, she is joking with other members of the community and even getting laughs when she loudly encourages her husband to get the family's slip of paper from the box. Prior to being selected, she defines herself in a socially prominent way. However, once it is clear that she and her family are selected, Tessie defines herself as a victim. She protests the lottery's procedure. When it is evident that she has been chosen, she defines herself as victim of a unfair and unrighteous practice. Tessie's self-definition is external. It shows the extent to which the lottery defines individuals. 

In both works, social reality plays a significant role in self-definition. External forces regulate the self-perceptions of Suyan, June, and Tessie.

Can someone describe Makepeace's character to me?

Makepeace is a complex character who changes significantly throughout Caleb's Crossing. He is the son of a local pastor and the brother of the main character, Bethia. Makepeace is a very religious young man who aspires to study at Harvard University. Despite his lofty ambitions, he is not academically gifted and has great difficulty achieving his goals. Makepeace is relatively close to Bethia and their sister Solace towards the beginning of the story, but his character development creates a schism in the family.

Makepeace fears the pagan influence of Caleb and his culture and is highly opposed to his relationship with Bethia. In fact, Makepeace grows paranoid and begins to blame Caleb for many negative events that happen throughout the story. He grows bold in his own authority as a young man living within a Puritan society and abuses his position. Eventually, his cruelty escalates to the point where he beats Bethia and reports her for using profanity.

As the story continues, Makepeace eventually undergoes some degree of growth as a person. He demonstrates family loyalty and a desire to make amends by keeping Bethia's secret about Anne. While Makepeace is not explicitly described as a villain, he does fulfill the role of the antagonist at multiple points throughout Bethia's story.

Does the big bang theory or the steady state theory explain the origin of the universe better? Why?

The big bang theory is currently the best theory of how the universe was created. 

The steady state model concluded that the observable universe was of a constant density because there was a source of matter in the universe generating new energy. At the time, the concept of matter being neither created nor destroyed was still new and contested. The theory of the big bang states that there is a constant amount of energy in the universe. All of this energy was created in the moment of the big bang.

There are several reasons the steady state theory is discounted. The first is the fact that the universe is changing. By looking through telescopes into deep space, we can see effectively into the past of the universe. At the furthest reaches of observable space, things are different. Radio wave-emitting stars, forming galaxies, and more varieties of stars can be found, suggesting a changing universe over time. 

The steady state theory is also discounted because of cosmic microwave background radiation. This field of radiation is almost strictly uniform in wavelength and direction, showing no point of origin. This implies there is no point where matter is being generated and no point where energy is being created. It also aligns with the theory of a cooling blackbody, which the big bang theory suggested.

Newer data today still refutes the concept of steady state. The recent discovery of gravitational waves is evidence of colliding supermassive black holes from the time after the big bang. Even the concept of Hubble's Law refutes the steady state theory, as stars can be observed to have velocities away from the point of observation proportional to the distance away.

The big bang theory explains the origin of the universe far better than the steady state theory.