In Heart of Darkness, why does Marlow describe Kurtz as a "universal genius"?

Marlow calls Kurtz a universal genius because of his take on humanity and his talents in a wide variety of subjects.
Marlow has been interested in Kurtz since he first heard about the man. He wasn't sure why Kurtz had so many people discussing him; he didn't know what the man's motives were or why he made the choices he did. It was difficult to separate the truth from the fabrications. Once Marlow met Kurtz, however, he was able to see more of the man himself.
Kurtz is never completely defined by Marlow. Marlow isn't sure what his primary interest and talent was because he was good at writing and at painting. Marlow says, "To this day I am unable to say what was Kurtz’s profession, whether he ever had any—which was the greatest of his talents." He hears of Kurtz as an excellent musician, a painter, and a potential politician. Kurtz's talents encompass a variety of spheres.
Marlow goes through a variety of feelings toward Kurtz but in the end, he believes the man's final words show that Kurtz had a greater understanding of himself and the world. This is something that Marlow acknowledges and admires.

Marlow mentions that Kurtz is a "universal genius" in the conversation that he has with Kurtz's cousin after Kurtz has died. Marlow is in the "sepulchral city," where the company's management is based, and Marlow says of Kurtz, "He was a universal genius—on that point I agreed with the old chap." Kurtz's cousin describes Kurtz as a musical genius, and Marlow realizes that he does not even know what Kurtz's profession was, though Kurtz had interests in writing, painting, and journalism.
In addition to possessing this broad range of talents, Kurtz seems like a "universal genius" because of his reported last words, which were, "The horror! The horror!" Marlow says of Kurtz's statement, "After all, this was the expression of some sort of belief; it had candor, it had conviction, it had a vibrating note of revolt in its whisper, it had the appalling face of a glimpsed truth." In other words, Marlow admires Kurtz because Kurtz, in his last moment of life, dared to make a bold admission and assertion that what he had witnessed of the European involvement in Africa was wrong. Marlow refers to Kurtz's statement as a "moral victory" that has been earned through defeat. That is why, Marlow says, he remains loyal to Kurtz and his memory. In the end, Kurtz admitted that what he had seen and done were travesties of enlightenment. 

Can the lottery be seen as a collective act of murder?

If the question is asking about the possibility of viewing the lottery system from Jackson's short story as collective murder, then I say the answer is yes.  I think the societal stoning to death of Tessie could be viewed as murder.  The town collectively works together and intentionally kills someone.  That sounds like murder to me.  
I suppose that a claim could be made that the lottery is not murder though.  Everybody in the town voluntarily participates in the archaic tradition.  Tessie knows that she has a chance of dying before the drawing even starts.  I suppose the claim could be made that it's not murder because, in a way, Tessie volunteered to die.  
I don't believe euthanasia is a possibility.  That's a "mercy killing."  Tessie is not suffering from anything; therefore, killing her doesn't relieve her of any pain.  I don't believe the lottery is suicide either.  Tessie might be participating in the lottery, but she most certainly does not want her life to end. 

"It isn't fair, it isn't right," Mrs. Hutchinson screamed, and then they were upon her.

I also don't believe the lottery system represents a justifiable form of capital punishment.  Capital punishment is the legally authorized killing of someone as punishment for a crime.  The lottery system from the story is definitely the legal authorization of killing someone; however, Tessie didn't commit any crimes.  If she didn't commit a crime, then capital punishment doesn't apply.  
Considering the above options of exactly what Tessie's death should be called, I believe that murder is the best choice of the group. It's even premeditated.  People show up to the lottery with rocks and stones picked out. They all know that if their name is not picked, they get to throw stones at a person until that person is dead.  Their actions are not accidental.  It's not manslaughter or even negligence. It's murder.  

What is the chemical equation for: hot iron reacts with hot steam to form iron(II,III) oxide and hydrogen gas is released?

Iron(II,III) oxide has the formula  Fe_3O_4, and water steam has the same formula as water, H_2O. Therefore the unbalanced equation has the form
Fe + H_2O =Fe_3O_4 + H_2.
To balance this equation, first look at  Fe: one at the left and 3 at the right. So give Fe at the left the coefficient 3. It becomes
3Fe + H_2O = Fe_3O_4 + H_2.
Then count oxygen O: 1 at the left side and 4 at the right side. Thus give H_2O at the left the coefficient 4:
3Fe + 4H_2O = Fe_3O_4 + H_2.
And finally take into account hydrogen H: 8 at the left, 2 at the right. So it is enough to give the coefficient 4 to H_2:
3Fe + 4H_2O = Fe_3O_4 + 4H_2.
Now the equation is balanced.
https://www.flickr.com/photos/lorenzoprostamo/8153639735

In Fahrenheit 451, what are some examples of allusions and authors?

In Fahrenheit 451, Bradbury makes reference to a lot of other books and authors. Here are a few examples:
There is a reference to the Oxford Martyrs, Hugh Latimer and Nicholas Ridley, who were burned for heresy in 1555. In fact, Latimer's words are quoted by the woman who is burned in Part One.
In Beatty's speech to Montag, in which he explains and justifies the fireman system, Bradbury refers to two other important works: Uncle Tom's Cabin by Harriet Beecher Stowe and Little Black Sambo by Helen Bannerman.
Just before Montag kills Beatty, there is a reference to Shakespeare, specifically to his Julius Caesar:

"There is no terror, Cassius, in your threats, for I am arm'd so strong in honesty that they pass by me as an idle wind, which I respect not!"

Shakespeare himself is mentioned by Montag when he calls Faber for the first time. Montag also mentions Plato, the philosopher, in this call.
Matthew Arnold's poem, "Dover Beach," also features in the book. It is read out by Montag and makes one of Mildred's friends cry.

When does Lady Macbeth go mad?

In the text, there is no specific moment in which Lady Macbeth goes mad. However, she is clearly of unsound mind by act 5, scene 1. In this famous sleepwalking scene, Lady Macbeth is haunted by the memory of her crime and is seen trying to wash invisible blood from her hands.
What is interesting about her madness is that it appears to come on gradually. In act 3, scene 2, for example, we see the very beginning of her torment and anxiety in the following quote:

Naught’s had, all’s spent,
Where our desire is got without content.
'Tis safer to be that which we destroy
Than by destruction dwell in doubtful joy.

What she's saying here is that killing Duncan wasn't worth it. Although she is queen, she is tormented by feelings of anxiety and remorse. Arguably, this is where her madness begins, with these very early feelings of guilt. Although she is able to keep these feelings under control in public, as we see in the banquet scene, her madness is inescapable by act 5, scene 1.

Lady Macbeth goes mad some time between the dinner party where Macbeth sees Banquo's ghost, and her sleepwalking scene.  The dinner with all the lords (in act 3, scene 4) is actually the last time that Macbeth and Lady Macbeth appear on stage together, and Lady Macbeth is quite anxious in this scene about her husband's mental state.  She feels that he is acting crazily: he is speaking to Banquo's ghost aloud, in front of all their guests, and it sounds to her as though he is addressing a hallucination of Duncan's ghost.  Macbeth says to the ghost, "Thou canst not say I did it.  Never shake / Thy gory locks at me."  Lady Macbeth fears that he is going to give them away as Duncan's murderers (as she does not know yet that Banquo is dead).  Her anxiety is so immense that she insults him, asking, "Are you a man?"  The implication is that he is not.  She scolds him, trying to get him to be quiet. When the lords start to ask him questions, she insists that they leave immediately.  In an interesting moment of foreshadowing, Lady Macbeth points out that Macbeth has not slept.  
It is ironic that she says this to him because, when we next see her, she has ceased to sleep peacefully too.  Lady Macbeth does not reappear until act 5, scene 1, following the murders of Lady Macduff and her children. In this scene, her servant has called a doctor to observe her strange, nocturnal habits.  At this point, she seems to be hallucinating, imagining that she cannot wash Duncan's blood off her hands, and she cries, "Out, damned spot!  Out, I say!"  She also refers to Macduff's dead wife, asking, "What, will these hands ne'er be clean?"  I interpret this progression to mean that she now knows that her husband has ordered the deaths of an innocent woman and her children.  She has created a monster and Macbeth has gone on to exact greater and crueler violence: first he kills Duncan, then he orders the murders of his best friend and his friend's son, and finally, he kills a good man's family.  When she asks if her hands will ever be "clean" again, the implied answer is no.  Perhaps she has recognized her role in the deaths of the innocents, and it has driven her mad.  At any rate, Lady Macbeth is certainly no longer mentally stable, and, when next we hear of her, she will have taken her own life.

How does Arthur Miller's play The Crucible invite audiences to consider the detrimental effects of a repressive society?

A section of the Salem community was persecuted based on superstition, religion, and personal vendetta. The power of religion over the people and the enforcement of the religious code on the community by the authorities made the society a repressive one. Individuals had no choice with regards to religious practice. They were expected to remain silent about their concerns on the administration of the church and religious practice in general. The people were also expected to go to church consistently, and failure led to suspicions of witchcraft. For instance, Hale suspected John after he unconvincingly responded to his questions about church attendance, his child’s baptism, and the Ten Commandments.
The author showed the detrimental effects of a repressive society by singling out the individuals who took advantage of the situation to forward and/or protect their interests. For instance, the issue of witchcraft was used by some individuals to get rid of their foes. Mr. Putnam used the situation to try and appropriate privately owned property by falsely accusing Giles. Judge Danforth failed to uphold justice and instead sought to protect his position. In conclusion, People in positions of power and those that can manipulate the situation have the last say in a repressive society.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 42

Find the $x$ and $y$ intercept of $\displaystyle y = x^2 - 5x + 6$


$
\begin{equation}
\begin{aligned}

y =& x^2 - 5x + 6
&& \text{Given}
\\
\\
y =& (x - 3)(x - 2)
&& \text{Factor}

\end{aligned}
\end{equation}
$


To solve for $y$ intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

y =& (0 -3)(0 - 2)
\\
\\
y =& (-3)(-2)
\\
\\
y =& 6

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0,6)$

To solve for $x$ intercept, we set $y =0$


$
\begin{equation}
\begin{aligned}

0 =& (x - 3)(x - 2)
&& \text{Zero Product Property}
\\
\\
0 =& x - 3 \text{ and } 0 = x - 2
&& \text{Solve for } x
\\
\\
x =& 3 \text{ and } x = 2
&&

\end{aligned}
\end{equation}
$


Thus, the $x$ intercepts are at $(3,0)$ and $(2, 0)$