When can the instantaneous velocity of an object equal the average velocity of an object? I understand that if acceleration is zero, motion is...

As pointed out in the question, with uniform motion (no acceleration) the instantaneous velocity and the average velocity are the same everywhere, as the object has a constant rate of change in regards to its distance traveled.

But there can be times when the instantaneous velocity and average velocity are the same even with varying accelerations. For example, imagine a 300 mile road trip which takes exactly 5 hours. The average speed (velocity if the trip is all in one direction) is 60 miles per hour. Your speed at any time of the trip could be 60 miles per hour; it might always be 60 miles per hour, or you might speed up and slow down.

This is the premise behind giving speeding tickets to vehicles whose speed has been measured indirectly. Some police utilize markings on the pavement and a flying spotter while others might time a trip between toll stations, etc., but they never measure speed directly. They infer that a vehicle that covers a distance faster than they could have covered it obeying the speed limit must have exceeded the speed limit. Further they know that the vehicle must have reached the average velocity during the trip.

Using ideas from calculus we can show that if the distance function can be modeled by a continuous (no breaks or asymptotes) curve with no corners or cusps over an interval from a to b, then there is a point c in the interval where the velocity (the instantaneous rate of change of the distance at point c) will be equal to the average velocity (the average rate of change over the interval).

You can see this graphically; the curve represents the distance function as a function of time while the line shows the instantaneous velocity for some points:

What does "My naked weapon is out. Quarrel! I will back thee" mean?

Throughout their banter in the opening lines of Shakespeare's Romeo and Juliet, the Capulet servants Gregory and Sampson make sexual references as they discuss how much they hate the Montagues and would like to engage them in a street fight. Sampson suggests that he would like to rape the Montague women, making a rude reference to part of his anatomy when he says, "’tis known I am a pretty piece of flesh." This same piece of anatomy is likened to a sword as Gregory urges Sampson to "Draw thy tool" as the Montague servants approach. Sampson does indeed pull his sword and again makes an overt reference to his anatomy when he says,

My naked weapon is out. Quarrel! I will back
thee.

A quarrel is a fight and the two servants do their best to goad the Montagues into an altercation. When Tybalt arrives a street brawl does break out among the bitter rivals.

How does Kino's perspective change throughout The Pearl?

In the beginning, Kino places great hope on the pearl, believing that it will change his future and that of his family. He believes that this will give him some freedom that he never knew he did not have. He was perfectly content before finding the pearl, but after his discovery he realizes that there are some things that will make his life (and those of his wife and child) much better. He begins to experience discontent. When he goes to the pearl merchants, he becomes cynical and skeptical, sure that they will try to cheat him (as indeed they do). He is not content with the price they offer. His discontent increases; the merchants in the city will give him a better price. He distrusts his wife, believing that she is trying to take the pearl away from him. More and more he doubts the honesty of those around him. All his trust is in the pearl, not in those around him, even those he loves. In the end, Kino loses his child and willingly gives up the pearl. It will not return his child to him, but he recognizes that it is the pearl that has brought such discontent into his life. His perspective has gone from contentedness and happiness to sorrow, doubt, and loss. He will not be able to regain all that he has lost; he hopes for merely a return to his simple life.

How would the story be different if it were told from Jim's prespective? Why does O. Henry choose Della's perspective?

Part of what makes this story by O. Henry work is the parallelism of the two characters as each tries to demonstrate his or her love to his or her spouse by giving the best possible Christmas present. Each gives up the possession of greatest importance to him or her in order to purchase something that would enhance the other's dearest possession. The beauty of the message is that their love for each other is equally matched. However, there is a sense in which Della's sacrifice was incrementally greater than Jim's. While Jim pawned a family heirloom that meant a lot to him, Della actually gave a part of herself, her hair. Della's hair was a part of her identity to a greater degree than Jim's watch was a part of his. Jim kept his watch in his pocket, and although he knew it was there, others would not know about it unless he pulled it out. Della's hair, on the other hand, was visible to everyone anytime they saw her. So one reason to tell the story from Della's perspective is that her choice was more difficult and more life-changing than Jim's.

Another reason to tell the story from Della's point of view is that women are, generally speaking, known for being more emotional than men, and telling the story from Della's perspective allows O. Henry to incorporate more pathos into his tale. Della cries and worries about how Jim will react to her new look. Jim's reactions are more reserved. Instead of sobbing, "Jim tumbled down on the couch and put his hands under the back of his head and smiled." A story written from Jim's perspective could be interesting and poignant as well, but it would not have the highs and lows of emotion that the story had when told from Della's perspective.

How did the U.S. Constitution succeed when the Articles of Confederation failed?

America's first formal attempt to organize itself as an independent country commenced with the adoption of the Articles of Confederation in 1781. This document reflected America's wariness over centralized authority and the tendency for governments to control and tyrannize their member states.

After recently separating itself from the oppressive control of the British, American leaders were in no mood to relinquish control to a governing entity of their own country. When they drafted and passed the Articles of Confederation, they made the federal government weak. Unfortunately, they also made it ineffectual in several important respects.

Taxation: The federal government could not levy taxes. America was struggling to repay war debts and could not do so without money. The Constitution provided means to tax, although the U.S. still did not have a federal income tax for many years. 

Executive Leadership: The Articles did not authorize the election or appointment of a national leader—a position we now refer to as a president. Without a national leader, it is difficult to organize and motivate member states to act in the national interest. The Constitution provided for the election of a president.

Trade: The weak federal government could not regulate trade with foreign countries, leaving states to make their own treaties. States worked against each other in this respect. There was also no national currency, which impeded interstate economic activity. The Constitution gave the federal government the power to negotiate trade deals with other countries and establish a national monetary system. 

These are just a few of the major problems associated with the Articles of Confederation. In 1789, the Constitution as we now know it was enacted. It greatly increased the power of the central government in all the areas listed above. 

In Shakespeare's A Midsummer Night's Dream, why does Nick Bottom want to play all of the parts in the play-within-a-play?

In Shakespeare's A Midsummer Night's Dream, Nick Bottom, the weaver, loves to be the center of attention. When he gathers with his fellow players at Quince's house in Act One, Scene Two, he is eager to derail the casting session with his silly demands. Bottom is happy to be cast as Pyramus in the players' production of "Pyramus and Thisbe," proclaiming that this tragic role will allow him to "move storms" in the eyes of his audience. At the same time, Bottom feels like he would be much more suited to play a tyrant or some role in which he could rant and rave. 

When Flute is cast as Thisbe, Bottom insists that he could play Thisbe as well by wearing a mask and speaking "in a monstrous little voice." When Snug is cast as the lion, Bottom demands, "Let me play the lion too," so that he may roar in a way that does "any man's heart good to hear me" and makes the Duke ask for him to roar again. Quince finally manages to convince Bottom to stick to his own part by claiming that Pyramus is the best looking man of all men. Flattered, Bottom seizes the role. 

This scene makes it clear just how pompous and self-absorbed Bottom is in believing that he could (or should) play all the roles in the play. It's a good insight into his character and a funny setup for the later payoff of the play when Puck turns him into the literal embodiment of his spirit: an ass!

What is the traditional tool used for sowing seeds?

In farming, the sowing of seeds is the act of planting them in the soil.  The soil needs to be broken up and aerated, the seed needs to be deposited in the loose soil, and then the seed needs to be covered with the loose soil.  In the era of modern agriculture, there are mechanized tools such as seed drills that can plant multiple seeds at once at precise depths and distances over and over again.  Seed drills are pulled behind tractors to cover large fields.  But the traditional hand tool used for sowing seeds is a hoe.  A hoe is a flat metal blade at the end of a wooden pole that a farmer can use to till the soil and then redistribute the soil to cover the seed after sowing.  This tool is still used by home gardeners and family farmers around the world.