What happens in the Battle of the Cowshed in the book "Animal Farm"?Im writing a newspaper article for coursework about the Battle of the cowshed...

The basic answer to your question is that, under Snowball's leadership, the animals are able to defeat an attack by the humans. They are attacked by Mr. Pilkington and Mr. Frederick, whose animals have become "unruly" when their animals heard of the rebellion. So, even though they don't usually get along, Pilkington and Frederick join forces and attack Animal Farm. Snowball has read a book about Julius Caesar and his military tactics so he organizes the battle and the animals win. The complete details of the battle are located in Chapter 4 of the novel. In the end, Snowball and Boxer are awarded the military decoration of "Animal Hero, First Class." Only one sheep is killed and it is awarded the distinction of 'Animal Hero, Second Class."

In Macbeth, how do Macbeth's reactions and conflicts in Act V affect our understanding of his character as the tragic hero?

By the conclusion of the play, Macbeth has evolved into a murderous tyrant with much innocent blood on his hands. He is despised by his own people who have risen up against him, supported by foreign allies. Had Macbeth always been so despicable, there could have been nothing heroic in his character, but this was not the case. In the beginning of the play, Macbeth had been a loyal and courageous general. Before Macbeth's death, Shakespeare gives us a final glimpse of him as he had been in order to emphasize the tragedy of his fall and destruction.

In Act V Macbeth wavers between fear and confidence. Surrounded and outnumbered, he calls for his armor, vowing "I'll fight, till from my bones my flesh be hacked." Yet he still feels security in the witches' final prophecy:

They have tied me to a stake; I cannot fly,

But bearlike I must fight the course. What's he

That was not born of woman? Such a one

Am I to fear, or none.

When he finally meets Macduff in battle, Macbeth's former heroic character is revealed briefly. Having slaughtered Macduff's entire household, he does not wish to kill Macduff himself. When he learns that the witches' prophecy won't protect him (Macduff was not born of a woman), Macbeth chooses to fight rather than surrender: 

I will not yield,

To kiss the ground before young Malcom's feet, And to be baited with the rabble's curse.

Though Birnam Wood be come to Dunsinane,

And thou opposed, being of no woman born,

Yet I will try the last. Before my body

I throw my warlike shield. Lay on, Macduff;

And damned be him that first cries "Hold, enough!"

Thus, in our last glimpse of Macbeth, he acts with courage and honor, which emphasizes the tragedy of his downfall and destruction.  

What is the meaning of "Thy root is ever in its grave"? What is the paradox?

A paradox is either a statement or group of statements that, at first, seem to contradict each other. Even though at first it may seem contradictory--they can't be true at the same time!--they do offer some unique perspective and they do offer up something that can possibly be true...so...

The root of a plant is its foundation, the source of the plant's life; however, in this sentence, the source of life for the plant is in a grave--death. This gives an interesting image because roots are in the ground and so are graves, yet the root is life and the grave is death.

What is the importance of the gravedigger scene in the story of Hamlet?

It's an absolutely key scene. Shakespeare is an absolute master at juxtaposing the comic with the dramatic: and the two gravediggers' comic dialogue which precedes Hamlet's entrance prepares the ground for real surprise when the same grave, only a few hundred lines later, becomes the site of an impassioned fight between Hamlet and Laertes.

It's often the name of the game in Shakespeare's "comic relief" scenes that the themes reflect in a comic way the wider themes of the play. Thus, the opening argument about whether Ophelia "drown'd herself wittingly" reflects the play's concern with suicide - as outlined earlier in the "to be or not to be" soliloquy.

The scene also achieves precisely the absurdity which baffles Hamlet: the juxtaposition of death with comedy. It's no accident that the gravediggers are designated as "First Clown" and "Second Clown". Thus we have jokes about the pre-eminence of death: the gravemaker's houses "last till doomsday." And death even visits Yorick in the scene - an absent clown, now just a skull, who Hamlet and the gravedigger remember as "a fellow of infinite jest, of most excellent fancy". Even funny men - even men who tell jokes - die.

It's a brilliant scene which focusses the theme of "death" ready for the play's final scene and Hamlet's death - and provides the final comic moment of the play before the denouement of the tragedy.

Would you help me with Whitman's "I Hear America Singing"?I need to put this sentences in my own words describing the job of each worker 1. Those...

To put something into your own words, or paraphrase it, you need to do two general things: you need to understand the meaning (first the literal meaning, and then any non-literal meaning), and then you need to express it in your own words.  Start with the first part. Does Whitman literally hear American workers singing? Maybe—maybe he's there on a day like a musical. However, it's more likely that he hears them working and talking, and he calls that a song. Therefore, you'd have to express that.
For each line, then, you'd essentially translate and express. The "mechanics" are manual laborers, and so on.

Review each sound that the workers would make, and how they have rhythm, etc.

Why are people's homes called dwellings in the book "The Giver"?

Probably the best answer for this is to compare the words "home" and "dwelling". A home implies a place where people care about each other, love each other, and are connected in a variety of deep ways. Dwelling, on the other hand, is simply a place where people live, a roof over their heads. To turn the question back to you, how does that difference relate to how deeply the people in Jonas' house really care about each other?

How would you describe the atmosphere of Lord of the Flies?

Golding's island, I would have said, is presented as a natural paradise, with extreme weather conditions, but, most significantly of all, it is regularly seen through the eyes of the boys themselves as something ominous, and rather threatening.

Early on in Chapter 1, Golding sets up the oppressive heat of the jungle:

...the jungle was a bath of heat. He was clambering heavily among the creepers and broken trunks when a bird, a vision of red and yellow, flashed upwards with a witch-like cry; and this cry was echoed by another.

"Witch-like cry", I always think, is a simile which must be meant to be heard through Ralph's ears: he is the one who makes the comparison in his head to a witch. And it has a sort of ominous, horror-movie energy about it which lays the ground for the beast to come later on.

The island, with its pink rocks, its candle-buds, and its deep lagoons is a place of magic. But there's also a sense that that magic can have some bite, some danger to it:

Some act of God— a typhoon perhaps, or the storm that had accompanied his own arrival— had banked sand inside the lagoon so that there was a long, deep pool...  The water was warmer than his blood...

It's a glorious warm pool, like a hot bath. Yet the way it is presented draws our attention to its origins in a scary storm, and makes an odd comparison between water and blood. And that sense of beauty tinged with danger is, I would say, the novel's atmosphere.