In Of Mice and Men, what is the impact of Steinbeck's stylistic choices in its opening and ending?

Steinbeck was quite insightful in bringing out the idea of
George telling Lennie that if there was any trouble, he was to "go and hide in the brush."  This
was introduced in the opening, when things were tough, but not as complex.  It was also
introduced at a moment where hope was emerging to its zenith.  The dream of the farm had already
been introduced, and both Lennie and George had already been depicted to be different than others
of the time period in their sense of community and shared experience with one another.  In
bringing both back to the brush at the end, Steinbeck has been able to bring a sense of the
complete to the narrative:

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The most important symbol in the novel is the
bank of the Salinas River, where the novel begins and ends. In the story's opening, when George
and Lennie come to the riverbank, it serves as a symbol of retreat from the world to a natural
state of innocence. In this first scene, George tells Lennie that he should return to this
riverbank if there is trouble at the ranch where they plan to work. The riverbank is a "safe
place" for the two characters.

The fact that both the
opening and ending begins with a naturalist view of the small pond is meaningful.  At the start,
Lennie and George were concerned with drinking water and whether it was "clean."  Now, their
situations have grown in complexity and their problems are much more intense.  I think that
Steinbeck brings out this intricacy in Lennie, himself.  The vision of Aunt Clara and the rabbit
from his own mind help to enhance the fact that the world is having an adverse effect on Lennie. 
Additionally, Lennie's refrain of "going into a cave" is challenged by his visions, suggesting
that he would have never had the strength to leave George.  In the end, the narrative comes full
circle because of ending it where it starts.  There is almost a Classically tragic feel to it,
almost as if Steinbeck is giving his characters a sense of regal nobility that the real world
would never grant to them.  In this light, Steinbeck himself might be doing right what the world
had done intensely wrong.

What are the length, slope and the midpoint of PQ for P(7,11) and Q(-2,4)?

P(7,11), Q(-2,4)

(1) To find the
length :

The distance betwen two ponits (x1,y1) and (x2,y2) is given
by:

d = sqrt{(x2-x1)^2 +(y2-y1)^2} .

So
the distance PQ = sqrt{(-2-7)^2+(4-11)^2} = sqrt{(-9)^2 +(-7)^2} = sqrt{81+49} =
sqrt130.

2) The slope m of the line joining the two points
(x1,y1)and(x2,y2) is given by:

 m = (y2-y1)/(x2-x1)
.

Therefore  slope of the line joining the line (7,11) and (-2,4)
is  given by: m = (4-11)/(-2-7) = -7/-9 = 7/9. So the slope is m =
7/9.

3)

The mid point of the two points
(x1,y1) and (x2, y2)  is  ((x1+x2)/2 , (y1+y2)/2).

Therefore the mid
point of  (7,11) and (-2,4) is ((7-2)/2 , (11+4)/2) = ( 5/2 , 15/2).

In the last chapter of Mrs. Frisby and the Rats of NIMH, who does Mrs. Frisby meet?

After the Rats move Mrs. Frisby's cinder block house out
of the path of the plowers, she watches in safety while the fields are plowed. After
that, with Timothy well enough to move, they cover over the entrance and walk to the
brook where they and other mice live during the summer. While collecting moss, she meets
up with a neighbor:

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...she saw one of her neighbors, a lady mouse
named Janice who, like herself, had four children. Janice ran over to talk to
her.

"You're so late getting here," she said. "We all
thought something must have happened to you."
(O'Brien,
Mrs. Frisby and the Rats of NIMH,
Amazon.com)

To keep the
secret of the Rats, Mrs. Frisby claims that her cinder block was safe the whole time,
and Janice accepts that as luck. Janice, like other minor characters, is more concerned
for her own well-being, and is only a little surprised to see Mrs. Frisby alive and
well; Janice's impact on the novel is mainly to convince Mrs. Frisby that while she has
to keep her secrets from the other mice, she should tell her own children, who deserve
to know how the Rats helped to save their lives.

Romeo and Juliet are referred to as "star-crossed lovers." Discuss the concept of predetermined/fate destiny and how it relates to the play.Romeo...

In Romeo and Juliet, Shakespeare presents a
world that Elizabethans believed was ruled by destiny. One's "fate" was
unavoidable."

There has been extensive discussion for hundreds of
years as to whether the lovers are victims of fate. Students in classrooms debate whether or not
Romeo and Juliet could have made different choices that might have allowed disaster to be avoided
at the end of the play.

Consider the prologue, where in the Chorus
(before Act I begins), it is announced that the story that will commence involves two title="star-crossed"
href="http://dictionary.reference.com/browse/star-crossed+lovers">star-crossed
lovers (whose doom is fated). Shakespeare presents us (the audience) with the concept that the
end of the play is cast in stone, unchangeable.

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Fate and fortune are closely related...both concern events
that are out of human control.

The
Elizabethan audience believed that fate controlled their lives, and the characters of the play
also reflect this concept. When Romeo and his friends discuss attending the Capulet party (and
remember Romeo is a Montague, the enemy), Romeo (in his discussion with
Mercutio) worries because of a dream he has had that foreshadows his own
death.

The audience of the time would have understood and identified
with this feeling, believing that free will was not what guided their lives but fate did: life
was a story written before they were born that could not be altered. Fate and luck (fortune) are
intermingled, and are discussed by Juliet, Friar Lawrence, etc. Though Romeo tries to fight fate
by committing suicide, in reality, Romeo simply fulfills his fate—according to Shakespeare.
Shakespeare points out to his audience the belief that no one can avoid his/her
fate.

Describe some things that happened as the characters tried to solve the problem in Ender's Game?

This sounds like a homework assignment, so I'll just give
you some tips to get you started. How you answer the question depends on which
character's problems you focus on.

In Ender's
Game, the human race is fighting against its own extinction. Earth is
threatened by a race of alien creatures called buggers. The adults in the book
manipulate Andrew "Ender" Wiggin into commanding the battle against the bugger threat.
They realize Ender has the potential to be a military genius, so they take him from his
family and send him to a military academy called Battle School in outer space. There,
they purposely isolate him from the other students in order to make him work hard to
become a leader among them. They present Ender with harder and harder challenges in the
form of military games. In the end, they set Ender to work playing a game of command.
Although Ender does not know it, he is really commanding an invasion against the bugger
worlds.

Ender has a different problem. He knows that the
buggers are out there, and that he has to fight them someday, but he never knows he is
actually fighting them until after he has defeated them. His main problem in the book is
that his teachers keep presenting him with challenges, and these challenges are very
dangerous. He struggles against social isolation, bullying, and stress. He has fights
with bullies and finds creative ways to win games when the odds are against
him.

To do your assignment, you first need to choose
whether you want to write about what Ender does, or what the adults do. Then look
through the book to find the specifics about those characters' actions. If you feel
overwhelmed when you look for major events in the whole book, start by reviewing a
summary (link below). You might also want to look at the analyses of the characters. If
you focus on Ender, you should read about Andrew Wiggin (link below). If you want to
focus on the adults, you should read about Colonel Graff, Major Anderson, and Mazer
Rakham (link below).

Find the integral of f'(x) = 3x^2 - 6x + 3 given that f(0) = -4

Given the derivative, f;(x) = 3x^2 - 6x +
3  

Also, given f(0) = -4.

We need to
determine the function f(x).

We know
that:

f(x) = integral f'(x) :

Then, let
us integrate f'(x)"

==> f(x) = intg
f'(x)

                = intg ( 3x^2 - 6x + 3)
dx

                = 3x^3/3 - 6x^2/ 2 + 3x +
C

==> f(x) = x^3 - 3x^2 + 3x +
C

But given that f(0) = -4

==>
f(0) = 0 - 3*0 + 3*0 + C = -4

==> C =
-4

==> f(x) = x^3 - 3x^2 + 3x -
4

When salt is placed on ice , the ice melts. Why?

A block of ice left undisturbed is in a state of thermal
equilibrium. There is a portion of the ice that melts to form water and at the same time an equal
amount of water solidifies to form ice. This establishes a state of equilibrium with the net
amount of ice remaining constant unless there is a change in the thermodynamic
conditions.

The addition of salt disturbs the equilibrium. Salt
dissolves in the ice that melts to water. Water, with ice dissolved in it, has a lower point of
freezing than pure water. Generally this applies to any solute that is added to water. All forms
of dissolved impurities in pure water decrease its point of
freezing.

This lowering of the freezing point does not allow an
equal amount of water to freeze again as the amount of ice that melts to form water. Hence salt
is able to melt ice.