What is the theme of "Piping Down the Valleys Wild"?

The main theme in this poem, originally titled “Introduction to the Songs of Innocence,” by William Blake, is of innocence and childish happiness. There is a child sitting upon a cloud, which calls to mind the image of a cherub or cupid in a renaissance painting. This child is “laughing” and tells the speaker to play and sing songs about lambs and happy cheer. The piper “piped with merry chear” and “sung the same again.” The child weeps with joy upon hearing these songs and then entreats the speaker to write these happinesses down in a book so that others may read. The speaker then fashions a pen out of a reed and writes these happy songs down so that “every child” may “joy to hear” (enjoy hearing them).
The language in this poem is simple—there is not dense imagery or a complicated plot. There are, however, two potentially religious allusions: the child on the cloud and the “song about a lamb.” William Blake had complicated opinions about organized religion; he rejected the orthodoxy of Christianity and created his own mythology to describe what he saw as the divine creativity inside humans. The child on the cloud and the lamb could, then, both be seen as allusions to the innocence of a Jesus figure without being explicitly religious. I have linked to an electronic version of this collection so that you can see the other poems and illustrations that accompany this piece.

What mistake did Brian make in the use of his hatchet?

After the tornado, Brian attempts to get his shelter repaired. As he's looking down the shoreline for wood, he notices the tail of the plane sticking out of the lake. It occurs to Brian that if the plane is still intact, he may be able to retrieve the survival pack. Brian constructs a raft and swims to the tail of the plane, where he uses the hatchet to cut into the aluminum. As Brian attempts to bend a piece of the aluminum, he drops the hatchet in the water. He immediately recognizes his mistake and recalls how important the hatchet has been to his survival. Luckily for Brian, he is able to dive deep into the lake to retrieve the hatchet. This time, as he uses the hatchet to cut the aluminum, he is much more careful with his prized possession.

What idea of death does Wordsworth convey in the poem "We Are Seven"?

In "We are Seven," Wordsworth uses the perceptions of an innocent young girl to convey an idea that the death of the physical body is not the end of a person's existence.
The speaker runs into an eight-year old girl with a wild, rustic air about her. He asks her how many brothers and sisters she has, and she explains to him that there are seven in her family. She includes in that number two that have gone to sea and two that are buried in the churchyard.
The speaker argues that if two are dead, there are only five siblings in the family. But the little girl will have none of that. The speaker insists that the two dead children are in heaven, but the girl talks of visiting their graves where she sews, knits, eats her supper, and plays with her brother John. The dead children are as much a part of her life as if they were alive. Death to her is not the end, just part of a larger continuum.

What is the name of the structures that pull a valve open and shut?

In the most generalized notion of a mechanical valve system, the open and shut operations are controlled by oblong lobes, called cams, that rotate on the axis of a connected shaft, called the camshaft. The rotation of the camshaft can be accomplished by any component that transfers mechanical energy, usually a moving belt or sequence of gears.
The cams and camshaft are mounted in a larger component called the engine block. Against each cam, the engine block pairs a small cylinder called a tappet. The tappets move up and down based on the rotational position of the oblong cams. Once the mechanical energy that begins in the belt or gears reaches the tappets, it's transferred to a rocker arm attached to each valve. It is the arm's rocking motion that depresses and releases the one or more valves, opening and shutting the flow channel.

How is revenge used in Sweeney Todd?

Sweeney Todd tells the story of Benjamin Barker, calling himself Todd, who exacts revenge on the corrupt Judge Turpin, the man who sent him to jail. Worse still, the judge raped Barker's wife, she died by suicide, and the judge adopted Barker's daughter, Johanna, now a teenager. It soon revealed that the judge plans to marry her.
Even as Barker is consumed by the idea of revenge, he turns his targets into literal victims of being consumed. As he starts on his vengeful path, unrelated people get in the way so he kills them too. Distracted from his chance to kill the judge while shaving him, he goes on a murder spree.
His landlady, Mrs. Lovett, is an eager accomplice, motivated by greed. She turns the victims' bodies into the meat for her delicious pie fillings, and sells them to unsuspecting customers.
One of the men Barker kills is Pirelli, a rival barber who tries to blackmail him after recognizing him as Barker. Trying to find his missing employer, Pirelli's assistant Tobias starts to get in the way so Mrs. Lovett locks him into her bakehouse. There he learns their grisly secret and escapes.
The play's resolution uses revenge to end the cycle of revenge. Barker learns that his wife had been alive, though mad, only when he kills her in her current state as a beggar. Intent on revenge, he had believed Mrs. Lovett's lies. He does manage to kill Judge Turpin, and then Mrs. Lovett too, but then Tobias immediately kills him--a full circle of vengeance.
Only his daughter Johanna and her true love Anthony escape the killings, but now she is an orphan.

What are three physical objects that the speaker focuses on in the beginning of Sonnet 130?

In the first three lines of Shakespeare's Sonnet 130, the three objects that the speaker compares to his lover are the sun, coral, and snow. In this ironic twist on a love poem, the speaker uses these objects to describe how his lover's eyes are nothing like the brightness of the sun, her lips faded compared to the red of coral, and her breasts dulled in comparison to the bright white of the snow. One might think that in using these comparisons that the speaker is saying that he is not truly in love with his mistress. However, the final lines of the sonnet reveal that he is, in actuality, very much in love with his mistress, and that her physical appearance does not define his love for her.

Was Lord Ullin able to help his daughter? Why or why not?

Lord Ullin is a very angry man. His daughter has run off with a chieftain—the Chief of Ulva's Isle, no less—and he and his men are in hot pursuit. If they should catch up with the eloping lovers, there's no telling what they'll do to them. Understandably, the Chief and Ullin's daughter are keen to get away, and they hastily instruct a ferryman to take them to the other side of Lochgyle, even though the water is dark and stormy. As the sound of Lord Ullin's men and their horses gets nearer and nearer, the storm becomes ever more violent.
Lord Ullin finally reaches his daughter on the far side of Lochgyle. But this shore is a "fatal shore," for Lord Ullin's daughter and her lover lie dead. Lord Ullin's anger turns to sorrow, and he loudly laments his loss as the waves crash against the shore. In retrospect, there was very little he could've done to save his daughter after she boarded the ferry. Once she was out on the loch in the middle of such a terrible storm, it would've been suicide for him to attempt any kind of rescue. But perhaps if he'd controlled his anger in the first place, then maybe his daughter wouldn't have eloped with her lover, and both of them might still be alive.
https://www.scottishpoetrylibrary.org.uk/poem/lord-ullins-daughter/