An object is being pulled with a magnitude of 87N. The direction of this force is 60 degrees above the x-axis. Calculate the x and y components.

To resolve a force into its x and y components, you have to use trigonometry.

If the angle that the force F makes with the positive x-axis theta then the horizontal component of the force is automatically F cos theta and the vertical component of the force is F sin theta.

So for this problem the horizontal component is 87cos60 which is 43.5N and the vertical component is 87sin60 which is 75.3N

The key to understanding how to resolve forces is to know that if you complete the parallelogram( in this case a rectangle) about the force or vector then sin theta = opposite/hypotenuse. IN this case the opposite side is the vertical component of the force and the hypotenuse is just the magnitude of the force or vector itself. So opposite = vertical component of force = hypotenuse x sin theta = F sin theta.

By similar reasoning, Horizontal component of force = F cos theta

What does John Proctor mean when he says that "God is dead" in Act 3 of The Crucible?

Proctor says this horrifying line after he has seen the awful power that Abigail, "a whore" (to use his word), has over Danforth and the court, after his wife, Elizabeth, has lied to save his name (making it appear that he was lying when he explained Abigail's ulterior motives for accusing Elizabeth), and after Mary Warren, his servant who he brought to the court to confess that the girls were actually "sportin'" when they made accusations, has turned on him and told the court that Proctor is "the Devil's man."  

When Proctor says that "God is dead," he means that God is no longer the ruling force in Salem anymore.  The Devil is now in charge, and he is working through these lying girls and this corrupt court to take innocent victims. Further, Proctor says,

A fire, a fire is burning!  I hear the boot of Lucifer, I see his filthy face!  And it is my face, and yours, Danforth!  For them that quail now when you know in all your black hearts that this be fraud-- God damns our kind especially, and we will burn, we will burn together!

Not only is the Devil, then, working through the girls and Danforth, but also through men like Proctor (and even, perhaps, Hale), men who knew (or suspected) early on that it was not witchcraft but spite and greed at the root of these accusations, and said nothing.  They have all welcomed the Devil in, and he lives now in Salem, not God.

What does James mean when he says "Great, now we have two of them to look after"? How does Captain Keller react to this? Why is this surpising?

When Annie Sullivan arrives at the Keller home, Captain Keller is apprehensive.  He does not like that Annie is young and had been blind until recent surgeries.  He makes comments about her being from the North.  His wife, Kate, tries to reassure him.  They have a discussion about the topic, with Kate speaking positively about Annie and Captain Keller expressing his doubts.  Then James jumps into the conversation, saying, "Great improvement. Now we have two of them to look after."  James is referring to the fact that Annie was blind and that Helen, her new student, is blind and deaf.  He is also expressing his opinion that Helen is a burden to him because of her disabilities.  Captain Keller is annoyed by his son's comment and snaps at him, telling him to go "look after those strawberry plants."  This is surprising because James had been reaffirming Captain Keller's own doubts about Annie Sullivan.

What is the symbolism of the ants that are consumed by fire as Henry turns the burning log?

In Chapter 41, the final chapter, Henry remembers seeing ants on a burning log right after he hears the devastating news that his child has been delivered stillborn. He meditates on the inevitability of death and thinks, "That was what you did. You died. You did not know what it was about. You never had time to learn." He thinks about ants he once saw on a log he put on a fire. He observed them scrambling to get away from the fire. While some were able to escape and head off in an unknown direction, most inadvertently went towards the fire: "Most of them went toward the fire and then back toward the end and swarmed on the cool end and finally fell off into the fire." The ants symbolize the inevitability of death; everyone around Henry will die (including Catherine shortly after this scene), and he knows that one cannot avoid death. People scramble to avoid death, much as the ants try to head away from the fire, but it catches up to them in the same way in which the ants, thinking they are heading away from the fire, wind up falling into it. Henry attempted to douse the fire with whiskey and only wound up steaming the ants to death, so his attempts at being a savior failed. He knows at this point that Catherine will also likely die, and there is nothing he can do about it.

Why is it important for experiments to be able to be repeated?

Being able to repeat experiments is important in many fields of science. The main reason that it is important for experiments to be able to be repeated is so that the same scientist, or other scientists, can conduct the exact same experiments and see if they are able to obtain the same results. This helps to validate that the previous findings are correct and did not occur due to some random factor outside of the experimental set up. Repeating experiments and getting the same results leads to further support of the original findings. Validation of repeated experiments is very important in all fields, but is especially important in fields like medicine. For example, if a group of doctors or scientists discovers that a certain drug can help cure an illness, it is important the experiments are repeated, and the same results are obtained before that particular drug is administered to the general public. Hope this helps!

What does the quote "And he will make the face of heaven so fine" mean in Romeo and Juliet?

Act III, Scene 2 of Shakespeare's Romeo and Juliet opens with Juliet's soliloquy (a long speech delivered directly to the audience without other characters on stage) anticipating the arrival of Romeo for their honeymoon night. His plan had been to climb into her bedroom with a tackled stair he had provided the Nurse earlier in the day. Throughout Juliet's speech, she is praising and personifying the night, calling it "gentle" and "loving." She wants the night to be recognized as greater than the day, as she imagines that when Romeo dies he will be cut "out in little stars/ And he will make the face of heaven so fine/ That all the world will be in love with the night/ And pay no worship to the garish sun." In other words, she believes Romeo is so striking and impressive that his image in the stars will make the night sky more attractive than the sun. She goes on to lament that although she is already married she has yet to enjoy the physical pleasures which marriage brings. Unfortunately, these amorous reveries are interrupted when the Nurse brings news that Juliet's cousin Tybalt was killed by Romeo.

What was Kino's reaction when he caught the scorpion?

The Pearl is a story rich in symbolism, and the incident with the scorpion is certainly no exception. Upon discovering the scorpion at the bedside of his son, Coyotito, Kino and his wife pray. Coyotito represent the innocent man, and the scorpion the malevolent forces of the world. The act of prayer seeks for the intervention of a considerate and compassionate force; unfortunately the force does not manifest itself and the scorpion falls on the child, stinging him.

Kinu captures the scorpion and kills it, representative of the rage that mankind often feels when the seemingly purposeless cruelty of nature strikes out at those who have done nothing to deserve their fate. Lacking any means by which to control such forces of evil, we are left with the negative emotions that accompany our helplessness.