Atticus says at the trial in To Kill a Mockingbird that "this case is as simple as black and white." What does he mean?

Atticus has known since the day he took the case that the
defense of Tom Robinson was not winnable. He tells his brother Jack (in Chapter 9)
that

"The jury
couldn't possibly be expected to take Tom Robinson's word agains the
Ewells'--"

The case boils
down to Tom's word against that of Mayella and Bob Ewell. Although the Ewells are the
"disgrace of Maycomb," they are white and Tom is black, and in 1930s Alabama, the word
of a white person is always believed over that of a black
person.

There is actually a double meaning in Atticus'
"black and white" statement. In one sense, he means that the case is "cut and dried":
The facts seem obvious. Atticus has seemingly proved that Mayella's attacker must have
been left-handed (as is Bob Ewell), and Tom's left arm is crippled. Bob and
Mayella's testimony conflicts with one another, and Mayella changed her story several
times while on the witness stand. Tom seems to tell his story truthfully and his
testimony seems plausible; the Ewells' testimony does not. But, as Atticus knows, the
trial all boils down to a white woman charging a black man with rape, and even Atticus
can't convince this jury to be colorblind in this case.

How does the discovery Chillingworth makes at the end of chapter X alter the relationship between the minister and him? Nathaniel Hawthorne's...

During Hester's interview with Roger Chillingworth of
Chapter IV in The Scarlet Letter, Hester is extremely anxious about
her old husband as she examines his face,

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"Why doest thou smile so at me?" inquired
Hester, troubled at the expression of his eyes.  "Art thou like the Black Man that
haunts the forest round about us?  Hast thou enticed me into a bond that will prove the
ruin of my soul?"

"Not thy soul," he answered, with another
smile.  "No, not thine!"

Thus
Hawthorne has foreshadowed the reaction that the physician has when, as Dimmesdale
sleeps, he moves the clothing that has always covered the minister's chest.  As he
stamps his foot on the floor in his Satanic delight, Chillingworth acts as
Satan

comports
himself when a precious human soul is lost to heaven, and won into his
kingdom.

Now, Chillingworth
does, indeed, possess the soul of the minister since he knows the secret sin that lies
within Dimmesdale.  This knowlege changes unalterably the relationship of the physician
and his patient.  For, Chillingworth becomes the fiend that holds the secrets of
Dimmesdale's soul, and he can manipulate and torture the minister now.  In Chapter XI,
Hawthorne writes,

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...the intercourse between the clergyman and the
physician, though externally the same, was really of another character than it had
previously been. The intellect of Roger Chillingworth had now a sufficiently plain path
before it.....Calm, gentle, passionless, as he appeared, there was yet, we fear, a quiet
depth of malice, hitherto latent, but active now, in this unfortunate old man, which led
him to imagine a more intimate revenge than any mortal had ever wreaked upon an
enemy.

Like Satan,
Chillingworth intends evil for the man who has provided him with the revelation he has
sought. As he has previously told Hester, "he will be mine," the physician makes plans
for torturing the minister and avenging himself as the cuckolded husband upon
Dimmesdale. Thus, Chillingworth becomes Dimmesdale's most deadly
enemy.

In Wuthering Heights, how does Heathcliff discover that Isabella is attracted to him?

The answer to this question can be found in Chapter Ten of
this excellent novel. Isabella, having confessed her feelings in a very petulant manner
to Catherine, then has to endure the shame and embarrassment of Catherine revealing them
openly to Heathcliff when he enters the house soon after to be shown in to a room with
both Catherine and Heathcliff in it. Note how Catherine greets
Heathcliff:

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"Come in, that's right!" excalimed the mistress,
gaily, pulling a chair to the fire. "Here are two people sadly in need of a third to
thaw the ice between them; and you are the very one we should both of us choose.
Heathcliff, I'm proud to show you, at last, somebody that dotes on you more than myself.
I expect you to feel flattered... My poor little sister-in-law is breaking her heart by
mere contemplation of your physical and moral
beauty."

Thus it is that
Catherine is the one to tell Heathcliff of his ardent admirer. She does this of course
with the chief intention of showing Isabella how ridiculous the idea of her union with
Heathcliff would be, but actually she underestimates Heathcliff and his desire to gain
revenge.

What are four sentences showing the steps toward the resolution of the problem?

The plot of a story is made up of five basic parts:
exposition, rising action, climax, falling action and resolution.  As part of the
exposition, an initial inciting incident is brought into the story.  This is an initial
conflict that basically gets the ball rolling and starts to make things happen in the
story.  For The Giver, the first important conflict is that Jonas
is chosen to be the new Receiver of Memory.

Since you ask
for four sentences, I will break them into the other types of plot after the initial
conflict that lead to the resolution.

The rising action of
the story is Jonas’s first experiences as a Receiver of Memory, when he learns that the
community’s memories will now be stored with him and he begins to see things he has
never known before, such as color.

The climax of the story,
when the conflict comes to its most serious point, is when Jonas watches the Release of
the newborn twin and he realizes that Release means death and the community kills anyone
who does not conform.

The falling action of the story is
when Jonas learns Gabe is to be released and decides enough is enough, and he and The
Giver plan his escape to Elsewhere with Gabe.

The
resolution of the story is a little tricky (because this story has an ambiguous ending),
but Jonas and Gabe either reach Elsewhere or they die in the
snow.

What does Uncle Jack's statement that "Her use of bathroom invective leaves nothing to the imagination" mean in Chapter 9 of To Kill a...

This quotation is spoken by Atticus' brother, Jack, during
the Finch family's Christmas gathering in Chapter 9 of To Kill a
Mockingbird. Scout had earlier gotten into a fight with her cousin, Francis,
in which she "split my knuckle to the bone on his front teeth." Uncle Jack had spanked
Scout, blaming her entirely for the altercation. Later, when Uncle Jack took care of
Scout's wounds in the bathroom after the two had made up, she asked
him,

"What's a
whore-lady?"

It was what
Scout had called Francis earlier, but she had no idea what the term meant; to her, it
was an innocent question. Jack's later statement that "Her use of bathroom invective
leaves nothing to the imagination," simply means that he was astonished at the young
Scout's question about such a demeaning and seemingly adult phrase. ("Invective," by the
way, is defined as the use of an insulting or abusive term.) Jack avoided answering
Scout's question directly, instead telling her a story about Lord
Melbourne.

What roles does judicial review play in our governmental system of checks and balances?

Judicial Review is the power of the Courts to declare Acts
of Congress or the States as well as of the President or other governmental officials to
be contrary to the meaning and intent of the Constitution. There is no specific
provision in the Constitution to provide for Judicial Review, but the power was inferred
by Chief Justice John Marshall in the case of Marbury vs.
Madison.

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The powers of the legislature are defined, and
limited; and that those limits may not be mistaken, or forgotten, the constitution is
written. To what purpose are powers limited, and to what purpose is that limitation
committed to writing, if these limits may, at any time, be passed by those intended to
be restrained? The distinction, between a government with limited and unlimited powers,
is abolished, if those limits do not confine the persons on whom they are imposed, and
if acts prohibited and acts allowed, are of equal obligation. It is a proposition too
plain to be contested, that the constitution controls any legislative act repugnant to
it; or, that the legislature may alter the constitution by an ordinary
act.

Between these alternatives there is no
middle ground. The constitution is either a superior, paramount law, unchangeable by
ordinary means, or it is on a level with ordinary legislative acts, and like other acts,
is alterable when the legislature shall please to alter
it.

If the former part of the alternative be
true, then a legislative act contrary to the constitution is not law: if the latter part
be true, then written constitutions are absurd attempts, on the part of the people, to
limit a power, in its own nature
illimitable

[T]he particular phraseology of the
constitution of the United States confirms and strengthens the principle, supposed to be
essential to all written constitutions, that a law repugnant to the constitution is
void; and that courts, as well as other departments, are bound by that
instrument

Since
the judges in this nation are sworn to uphold the Constitution and are bound by its
terms, any act or law found to be violative of the Constitution is unenforceable by the
Courts. The Courts thus have a powerful check on the other branches of the government as
they have the ability to stop their actions completely. Importantly, if the courts
determine that laws or acts violate the Constitution, the Courts decision can only be
reversed by amending the Constitution. There have been many attempts to amend the
Constitution to circumvent Court holdings, but they tend to fail
uniformly.

How could we identify the similarities between Ethan Frome and Willy Loman as tragic heros?

I will answer your question based on traits in order not
to discuss both characters separately in too much detail (which would be two different
questions).

The trait of the tragic hero involves a series
of events that occur to a character who inevitably has to deal with them. There is no
outside control nor help from fate that could prevent a tragic hero from a sad ending.
It simply is as if destiny has chosen to make the character suffer because of a tragic
decision or a tragic flaw.

This being said, Ethan Frome
would perhaps fit the tragic hero characteristics better than Willy Loman. This is
because the tragedy of Ethan Frome is his inability to change his life from a tragic
flaw. He has a series of tragic obstacles that include his diminished financial
resources, the influence of his wife, his lack of freedom, the intense emotion he feels
for Mattie, and, finally, his accident, which leaves him
disabled.

Ethan does not have many options to turn his life
around, nor to start over in a different direction. His biggest tragedy is that he knows
that he has a dream, and that he cannot make it happen no matter how hard he tries. The
accident that he suffers in the end is the best evidence of this: He could not even
complete a suicide- fate wants him to live for the rest of his life in complete and
abject misery.

Contrastingly, Willie Loman at all times has
a chance to give up his dream and go with what he really loves. He has signs all over
the place telling him that he is chasing waterfalls. He is well in charge in his
marriage and even takes in a mistress just to justify his egotism. Willy got what he got
because he basically built his path towards a sad ending, not because something is
hovering about his existence but because of tragic
decisions.

Therefore, metaphysically speaking, Ethan Frome
may the true tragic hero from a flaw, whereas Willy is also a tragic hero but from
decisions.