How would I compare the book Oliver Twist to the play Macbeth?

What an interesting analysis you have chosen or been
given! If I were you, I would want to approach this question looking at the topic of
evil and how we are or aren't susceptible to evil in our lives. This to me seems to be
the most obvious way we can compare these two excellent
texts.

Macbeth, of course, is famous
for the way in which Macbeth is driven into acts of murder by the prophecy he has
received from the witches and then the encouragement of his life. His ambition is the
cause of his increasing evil, that begins with murder and then ends with orchestrating
the death of entire families, as in the family of
Macduff.

However, let us compare the characters Macbeth and
Oliver from Oliver Twist for one moment. Oliver is noteworthy
precisely because of his goodness and innocence. In spite of the best efforts of evil
characters such as Fagin and Bill Sykes, Olvier remains uncorrupted and an essentially
good boy. Of course, critics argue that his character suffers as a result, as he remains
a flat, static character, and thus some argue he is unrealistic. However, it is
interesting that nothing is able to shake the innocence and naivety from
Oliver.

So, this is the way that I would approach this
question. A possible thesis statement you could use would
be:

Both Macbeth and Oliver
Twist explore the concept of evil how outside influences impact, or fail to
impact, their central characters.

This seems a really
interesting analysis. Good luck!

Discuss figurative language in "The Frog and the Nightingale."

I would say that one of the best examples of figurative
language would involve the imagery of Seth's description of the nightingale's song. 
When he uses the line, "as she serenaded," it represents several explorations of
figurative language.  The metaphor of the serenade is something that captures the
reader's imagination as it reflects love and a connection with the audience.  This image
is in stark contrast to the frog's attempts at singing.  At the same time, the image of
"serenading" reflects the pure beauty of her voice.  I think that another example of
figurative language is evident when the frog's training of the nightingale requires her
to "journey" up and down the scales of music.  The use of the term as a very reflects
the arduous and actually abusive lengths to which the frog goes to ruin her voice, under
the guise of mentor-ship and teaching.  The idea of "journeying" through the scales
reflect a pure sense of difficulty, reflecting what the frog wishes to do to her voice
in order to consolidate his own power.  In these examples, the use of specific terms
allows the figurative language elements of the poem to take over the reader's
perception, allowing a greater connection to be formed between the reader and what is
happening in the poem.

Does Rosalind overshadow Celia in "As You Like It?" How?

Rosalind definitely overshadows Celia throughout the play.
Rosalind is a major character, while Celia is only a minor character who exists partly
to provide opportunities for dialogue which informs the audience of important plot
developments, such as the fact that Rosalind is in love with Orlando and that Rosalind
intends to join her banished father in the Forest of Arden. Celia's father recognizes
that Rosalind overshadows his daughter. He tells her: "She is too subtle for thee; and
her smoothness, / Her very silence and her patience, / Speak to the people, and they
pity her. / Thou art a fool. She robs thee of thy name, / And thou wilt show more bright
and seem more virtuous / When she is gone." It is because Rosalind is the stronger
character that she chooses to disguise herself as a man when the two young women travel
together. Rosalind makes all the decisions and acts as protector of Celia. Both
characters, of course, were played by young males. No doubt the one who played
Rosalind/Ganymede was older and taller than the boy who played
Celia.

In Shakespeare's Julius Caesar, what is different about Brutus at the end of the play?

It appears that by the end of Shakespeare's
Julius Caesar that Brutus has lost sight of his purpose in killing
Caesar, may be suffering from remorse while he tries to convince himself of his noble
purpose, and that he makes some poor decisions with regard to the battle between his
army and Antony's.

The only reason that Brutus agreed to
help murder Caesar is that he feared when Caesar became king, he would change, and that
it would harm Rome. Brutus puts the good of Rome before his own good. However, he seems
to struggle with that decision throughout the play: he loved Caesar almost as much as he
loves Rome.

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...it is within the anguished workings of
Brutus's mind that the issue of tyranny versus freedom is played
out.

It is possible that
Brutus sees the outcome of Caesar's murder differently than he had imagined. Even while
he addresses the people of Rome defending his actions and they initially agree with him,
Mark Antony is a powerful speaker who turns the hearts of Rome's citizens against
Brutus. Then civil war breaks out. This certainly cannot be what Brutus had hoped for in
guaranteeing Rome's welfare.

Brutus and Cassius's agreement
to kill Caesar is based on Cassius' lies; they begin to fight—Brutus must know that
Cassius does not care for Rome as much as he cares for himself. Brutus continues to
insist that his actions were motivated by his love of Rome. Then he hears of his wife,
Portia's, suicide. This is another blow.

Even when Cassius
suggests that they fight when their army is well-rested, Brutus (for some fateful
reason) disagrees, and then attacks Antony's army too
soon.

It has
been suggested that...Brutus[ is unable] to distinguish his own motives from noble
principles.

Brutus is a man
who believes that anything done for the good of Rome is a noble cause. He enters into
the conspiracy to kill Caesar with earnest and honorable intentions, at least as
he sees it. However, Brutus loves Caesar and sacrifices the life of
his ruler for his "republican" principles. He murders the leader of Rome, which is
dishonorable—it would seem even as Brutus struggles to convince himself that he was
justified in his actions. Throughout the horror of the murder, civil war, conflict with
his "compatriots," the loss of his wife, and struggles with making the correct
decisions, perhaps Brutus is unable to "have his cake and eat it too." One is honorable
by acting with honor. It seems impossible to me that dishonorable behavior can be
justified by an "honorable" man.

Although Octavius provides
a soldier's burial for Brutus, and even Antony praises him by saying that Brutus was a
great and honorable man—the essence of a real man—that Brutus cannot believe these
things of himself. Antony says of Brutus:

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This was the noblest Roman of them
all.

All the conspirators, save only he,
(75)

Did that they did in envy of great
Caesar;

He only, in a general honest
thought

And common good to all, made one of
them.

His life was gentle, and the
elements

So mix'd in him that Nature might stand up
(80)

And say to all the world, “This was a
man!”

Brutus follows his
heart for Rome's sake, but perhaps it would have been better to consult his
conscience—his moral compass—as well.

In 1933, 3 milliion workers belonged to unions; in 1941, 8 million did. How and why did Americans unionize?

The main reason for the change that you mention here is
the New Deal.  Specifically, the increase in union membership is due largely to
President Roosevelt's policies towards unions.  The most important of these policies was
the passage of the National Labor Relations Act.

Workers in
the United States unionized because they wanted to have better working conditions and
higher wages.  This is not surprising.  The real issue is why they unionized so much
during the time that you mention.  This is due to the fact that the passage of the NLRA
protected their right to unionize in ways that had never been done before.  This allowed
union membership levels to rise dramatically.  As the link below tells us, this law
(also known as the Wagner Act)

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protected the right of workers to join unions.
Workers could no longer be fired for joining a union. It prohibited companies from
certain unfair business practices, such as interfering in union activities, refusing to
bargain with a union, or gaining control over a labor
organization.

Because of
these protections, workers unionized in large numbers during the New
Deal.

Ariel Dorfman’s “Hope” What questions does the story raise in your mind?

In Ariel Dorfman's poem, "Hope," from his collection of
poetry entitled, "In Case of Fire in a Foreign Land," I have many
questions.

The first question that came to mind when I read
the first lines (the first time) was how old was the son? My first reaction was that it
was a boy, but though it's not impossible, I would think that if these "people" are
looking for information, a child would generally (not always) have little to
tell.

My second question was where this event took place.
The use of the word compañero indicates that it is in a Spanish-speaking country.
Dorfman's biography indicates that it could be in Chile, where he and his family have
spent a great deal of time. I'd like to know for sure. I'd also like to know when this
happened?

I assume that, based upon the author's dedication
that the story is about Edgardo Enriquez Sr., his wife, and their son, Edgardo, Jr.,
which is something I wondered before I read the poem again. What really makes me wonder
is: was he still alive eight months later? And was he released and reunited with his
family? I wonder where they are now, regardless of what happened, and if they have been
able to move on and make any kind of life for
themselves.

Lastly, I wonder if Dorfman knew the family
personally, or only heard about them, and has he kept in touch?

How to solve the inequality sin2x>sin4x, if 0=

First, we'll have to move sin 4x to the left
side:

sin 2x - sin 4x >
0

The difference of the matching trigonometric functions
returns the product:

sin 2x - sin 4x = 2
sin[(2x-4x)/2]*cos[(2x+4x)/2]

sin 2x - sin 4x = 2
sin(-x)*cos(3x)

Since the sine function is odd, the
function sin(-x) = - sin x

sin 2x - sin 4x =
0

We'll re-write the
equation:

-2 sin(x)*cos(3x) =
0

We'll cancel each
factor:

sin x = 0

x =
(-1)^k*arcsin 0 + k*pi

x =
k*pi

cos(3x) = 0

3x =
+/-arccos 0 + 2k*pi

3x = +/- (pi/2) +
2k*pi

x = +/- (pi/6) +
2k*pi/3

Now, we'll see where the functions sin x and cos 3x
are both positive, or both negative, for the product to be strictly
positive.

The functions sine and cosine are both positive
in the 1st quadrant, and they are both negative in the 3rd
quadrant.

sin x = 0 => x = 0 (1st
quadrant)

sin x = 0 => x = pi (3rd
quadrant)

cos 3x = 0 => 3x = pi/2 => x = pi/6
(1st quadrant)

cos 3x = 0 => 3x = pi + pi/2
=> x = pi/3 + pi/6

x = 3pi/6 => x = 3pi/2
(3rd quadrant)

For the inequality to hold,
the values of x belong to the reunion of intervals
(0;pi/6)U(pi/2;5pi/6)U(3pi/2;11pi/6)