What effect does the temperature of nitrogen gas have on the pressure it exerts?

Nitrogen approximately follows the ideal gas law which
gives the relation between pressure and temperature as pV= nRT, where p is the absolute
pressure of the gas; V is the volume of the gas; n is the amount of substance of the gas
in moles; R is the gas constant (which is 8.314472 J*K^-1*mol^-1 in SI units); and T is
the absolute temperature.

Therefore from pV= nRT, we get p
= nRT / V. So as the temperature increases, for the volume and amount of the gas
remaining constant, the pressure exerted increases and as the temperature decreases, the
pressure exerted decreases.

why put NaOH and copper sulphate in protein solution to test for proteins?what reactions do these chemicals have with the protein solution that...

To test for proteins a BCA assay can be used. This test is
performed with a stock BCA solution which contains Bicinchoninic acid, salts of sodium
and Cupric sulfate pentahydrate in a solution with a high
alkalinity.

During this test, when the BCA solution is
added to proteins the peptide bonds in the proteins reduces the Cu 2+ ions to Cu 1+
ions. This reduction is dependent on the amount of protein in the solution. Following
this, two molecules of bicinchoninic acid chelate with each of the Cu1+ ions, and form a
purple-colored product which strongly absorbs light at a wavelength of 562
nm.

Looking at the absorption spectra after the chelation
and comparing it with solutions with a known protein concentration allows us to
determine the protein concentration in the solution being
tested.

What are some ways Danforth shows pride in the short story The Crucible?

In The Crucible, Judge Danforth
exhibits excessive pride and arrogance through his actions, his words, and his
attitude.  Three specific moments, all in Act III, are indicative of those
attributes.

One is when Danforth plays rather fast and
loose with the law.  We know the girls have eaten with some regularity with the judges;
and, while perhaps the court did not have the official status of the court system today,
the court was powerful enough to execute the guilty and should not have been so
comfortable with the accusers.  When Giles Corey comes to court, Danforth can't seem to
make up his mind whether official courtroom procedures should be followed or not.  When
it suits him, they do; when he'd prefer to ignore them, they don't. He says, "The pure
in heart need no lawyers."  Obviously, in this courtroom that's not true.   Clearly
Danforth sees himself both as being the law and being
above the law.

Another way Danforth
demonstrates his pride is in his dealings with Proctor.  Despite the fact that Proctor
virtually signs his own death warrant by admitting to adultery, and despite the fact
that Abigail actually leveled a not-so-veiled threat to cry witchcraft on Danforth
himself, Danforth is unwilling to recognize the fact that Elizabeth may have lied in an
attempt to save her husband from the gallows.  This is a moment of true revelation for
Reverend Hale, who quits the proceedings for good; but for Danforth there is no
bending.

The final incident of Danforth's pride and
arrogance occursin the final scene at the jail.  Rev. Hale has reappeared to try to save
innocent lives, and even Parris has come to plead for some grace on their behalf.  Hale
appeals to Danforth reasonably, asking him to simply delay the executions.  Danforth's
tirade makes it clear he will not bend, for he is God's voice on earth.  In fact,
earlier in this act, Danforth has the audacity to speak as one gifted with God's
authority:

readability="6">

John Proctor, I've seen your power. You are
combined with
ANTI-CHRIST!

Danforth
never bends and never admits he is wrong or even could be wrong. 
Never.

What does the following quotation mean: "There are times...when one must lose a little beauty if one is to keep what little beauty one already...

The quote "There are times...when one must lose a little
beauty if one is to keep what little beauty one already has," from "The Flying Machine,"
by Ray Bradbury, is a paradoxical statement. The Emperor is responding to his desire to
keep things the way they are in his kingdom in ancient
China.

The flying machine, invented by the man who is
brought to the palace, allows mankind the opportunity to enjoy the world's beauty as
never before. However, the Emperor is fearful that someone might use the machine for
something other than its access to the world's beauty. For instance, someone might try
to fly over the Great Wall of China, an evil intent as the Emperor sees
it.

The Emperor also does not want the word he knows to
change, so he is willing to sacrifice the beauty brought by the flying machine to
preserve the world he so enjoys—in the beauty he has created and
maintains, especially in his invention of the mechanical box with the miniature trees
and birds within it.

What is the significance and theme of the work?

“The Cask of Amontillado” is one of the best-known Poe
stories. All the characteristics of Poe’s fiction are there: an unusual and bizarre
setting, a disturbed narrator, a lurid and therefore arresting antagonist, and an act of
deliberate and depraved cruelty. According to Poe’s theory of the brief prose tale, it
is clear that his main concern in “The Cask of Amontillado” is to hold the reader’s
attention and emotions in a mood of both disbelief and amazement. Poe’s development of
the weird character of Montresor and the ghoulish setting are to be judged as they
contribute to the story’s impact. If readers silently protest that “this can’t be
happening,” “the narrator is not going to wall in Fortunato alive, and leave him,” then
Poe would have said that his story was a success as a brief prose
tale.

Find the length of the graph of f(x)=(1-x^2)^1/2 on [0, b]

We'll use the formula of calculating the length of the
graph:

L = Int sqrt{1+[f'(x)]^2} from x = a to x =
b

In our case a = 0 and b =
b

The length of the graph of f(x) = sqrt(1-x^2)
is:

L = Int sqrt{1+[(sqrt(1-x^2))']^2}dx , from 0 to
b.

We'll calculate the derivative of
sqrt(1-x^2)

[sqrt(1-x^2)]' =
-2x/2sqrt(1-x^2) 

[sqrt(1-x^2)]' =
-x/sqrt(1-x^2) 

{[sqrt(1-x^2)]'}^2 =
x^2/(1-x^2)

We'll add 1 both
sides:

1 + {[sqrt(1-x^2)]'}^2 = 1 +
x^2/(1-x^2)

1 + {[sqrt(1-x^2)]'}^2 = (1 - x^2 +
x^2)/(1-x^2)

We'll eliminate like
terms:

1 + {[sqrt(1-x^2)]'}^2 =
1/(1-x^2)

L = Int dx/(1-x^2)

L
= arcsin x from x = 0 to x = b

L = arcsin b - arcsin
0

L = arcsin
b

The length of the graph of
the function f(x) = sqrt(1-x^2), over the interval [0,b], is L = arcsin
b.

Which text did Shakespeare use to base Julius Caesar on? What changes did he make and why?

The primary source for Shakespeare's Julius
Caesar is Plutarch's Lives.  He concentrates on the
Caesar, Mark Antony, and Brutus.

Although Plutarch is his
source, Shakespeare uses the information about these three men to weave a compelling
story about Rome and the change that took place from a Republic to an Empire.  He
doesn't try to pass judgement but he presents the
events.

In a history book, we can read about these events
but Shakespeare puts a human face on the major players.

He
also uses the play to ask important questions.

How does one
stop Caesar from destroying the Republic since the people (mob) want to crown him king? 
Is the majority always right?  Does a war, in this case a civil war, resolve anything? 
Does anybody win?

Shakespeare uses the information gained
in Plutarch to spring board into these and other important
questions.