If vector a = (x^2-7, 27) and vector b = (x+3, -9) are parallel vectors in R^2, determine the value(s) of "x".

Vector a = (x^2-7, 27) and vector b = (x+3, -9). The two
vectors a and b are parallel when the coefficients of the x and y components of the
vectors are in the same proportion.

For the same to happen
(x^2 - 7)/(x + 3) = 27/-9

=> -9*(x^2 - 7) = 27*(x +
3)

=> x^2 - 7 = -3(x +
3)

=> x^2 - 7 = -3x -
9

=> x^2 + 3x + 2 =
0

=> x^2 + 2x + x + 2 =
0

=> x(x + 2) + 1(x + 2) =
0

=> (x + 1)(x + 2) =
0

=> x = -1 and x =
-2

The variable x = -1 and x =
-2

Is there a law that states how often a landlord is REQUIRED to put in new carpeting?I live in Michigan if that makes a difference at all. ...

There may be a specific law in Michigan that requires as
much; but I seriously doubt it. As a general rule, the Landlord has no obligation to the
tenant other than to ensure his quiet enjoyment of the premises, not misrepresent the
condition of the premises, and ensure that they be kept reasonably safe. Repairs, etc.
are often matters of negotiation between landlord and tenant and are usually written
into the terms of the lease. It is to the Landlord's advantage to keep the premises in
good repair as it makes it easier for him to rent the premises and receive a reasonable
return on his investment. Contrary to what you may have heard, tenants normally have an
obligation to return the premises to the Landlord at the end of the lease in the same
condition they received it, reasonable wear and tear excepted. If the last tenant left
the premises in good order, subject to reasonable wear and tear on the carpet, the
landlord is under no obligation other than not to misrepresent the condition of the
premises.

What two reasons did Montag give for burning the books in 1984?

If you are referring to the conversation between Montag
and Clarisse at their first meeting, his reasons are simple:  It's against the law to
have unapproved books and it's fine work that he enjoys.  The sense we get of Montag
early on is of someone who hasn't thought independently in a long time, perhaps his
whole life.  The work of a fireman makes sense to him.

He
mentions how he likes the smell of kerosene on his clothes, the schedule, the black and
white rationale of it all.  Clarisse is the problem with this.  She interrupts his
regimented, flaming, detached life with simple, yet troubling, questions such as "Are
you happy?".  Montag is forced to reevaluate whether he likes his job, his life, and the
answers for him become complicated.

Explain the myth of pre-history.

The "myth of pre-history" is an idea used by some scholars
of indigenous, non-European cultures.  It is an idea that is used to combat the
Eurocentric idea that only Europeans (and possibly a few others) were truly able to
create history and civilization.

Scholars who talk about
this myth argue that Europeans see other cultures as backwards and primitive.  Europeans
see cultures that did not develop literacy and, thereby, written histories and they say
that those cultures are primitive and less developed than those (largely European)
cultures that did create written histories.

By calling this
the "myth of pre-history" scholars are arguing that pre-literate societies that had no
written history were not more primitive than other societies.  They argue that this myth
has simply been created as a way of justifying European dominance of other
cultures.

What are the reasons for considering the murder of Polonius as the turning point in the play Hamlet?

You are right in identifying that Hamlet's murder of
Polonius is a very significant turning point in the play. Firstly, let us remember that
this is Hamlet's first act of open violence in killing somebody. Following "The
Mousetrap," now Claudius understands the true danger that Hamlet represents to his
person. Note what he comments to Gertrude in Act IV scene
1:

His
liberty is full of threats to all,

To you yourself, to us,
to every one.

Claudius
realises the way that Hamlet's presence threatens his own life and power, and continues
to act to do away with him, and thus the murder of Polonius represents an escalation in
the conflict between these two characters.

In addition,
this scene is important because of the way in which Hamlet confronts his mother after
killing Polonius, and makes her see the impropriety of her actions and doubt her
husband. This represents the first break in the relationship between Claudius and
Gertrude, who up to this point in the play had been united in purpose. Gertrude in Act
III scene 4 agrees not to sleep with Claudius any more and obviously begins to side with
Hamlet.

Lastly, let us remember how the murder of Polonius
impacts Ophelia and Hamlet's relationship with her. The madness of Ophelia as
demonstrated in Act IV scene 5 and the way that her father's death at the hand of her
lover has made her "importunate" and "distracted" is of course key in the way that
Laertes comes to side with Claudius against Hamlet, leading to the final tragic duel
that kills them both.

Comment on the conflicts in "Araby."

It seems to be that the biggest conflict in this story is
actually an internal one in the narrator himself, as his sense of romance, innocence and
naivety is confronted with the cold, harsh realism of the final events of this tale.
Note how the narrator describes his feelings for Mangan's sister, and in particular how
he gives them religious connotations:

readability="8">

These noises converged in a single sensation of
life for me:  I imagined that I bore my chalice safely through a throng of foes. Her
name spran to my lips at moments in strange prayers and praises which I myself did not
understand. My eyes were often full of tears (I could not tell why) and at times a flood
from my heart seemed to pour itself out into my
bosom.

The extent to which he
has taken his love is clearly shown here. It is so important that it has become
something sacred to him, and his emotions rule him. However, when he begins his
much-longed-for journey to the bazaar, it is clear that his dreams and imagination
receives a cold, sharp shock by the reality of the bazaar. As the lights are turned off
inside, he experiences a sudden epiphany:

readability="6">

Gazing up into the darkness I saw myself as a
creature driven and derided by vanity; and my eyes burned with anguish and
anger.

In the internal
conflict between romance and realism, realism has won out and the boy leaves a wiser, if
not sadder, individual.

why do the boys fight?

The boys fight because in their "society," aggression is
the answer.  The story is set in a time well before peer counseling and mediation.  It
is also set in a time when children were not given credence or validation as they are
today.  Without the proper "skills," such as peer counseling and mediation, youngsters
sometimes reacted with gut reactions, hence, physical aggression.  In addition, poverty
contributes to aggression.  Although I do not think that poverty is the issue in The
Outsiders.  The wealthy kids in the community were physically aggressive as
well!

So, in a nutshell, the times lent themselves to
aggression.  The United States was in the middle of a war.  The president had recently
been assassinated.  Cuba was a threat to the United States.  The nation was deeply
divided.  I think kids feel helpless in times of political strife as in "What can we
do?" and fighting may serve as an outlet for their frustrations.