Why did kids start to color their hair purple or paint their nails green?

Kids start coloring their hair purple and coloring their fingernails and toenails green as a way to express their individuality. The kids across the school begin doing this because they have been inspired by Stargirl and her individuality and actions. When Stargirl first arrived, she was viewed as a crazy person. Some students believed that she acted the way she did in order to attract attention to herself; however, they eventually realized that Stargirl acted the way she did because that was just her. Stargirl's confidence in herself and love toward everybody began catching on among the students in the school. Chapter 9 has students awaking like "mud frogs" in the rain. They begin exploring their individuality and encouraging pretty much anybody and everybody else in anything and everything that happens.

Can you help me with the first three lines of "Ithaka"? I need to write an essay with a clear topic sentence that explains what I think the first three lines mean.

The island of Ithaka, which in English is usually spelled Ithaca, was the homeland of Odysseus, its king, as depicted in the Iliad and the Odyssey by Homer. The Iliad tells of the part Odysseus plays in the Trojan War, and the Odyssey deals with Odysseus's ten-year journey home to Ithaka after the war was over. In the poem "Ithaka," C. P. Cavafy makes references to this voyage. For instance, the Laistrygonians, the Cyclops, and the angry god Poseidon were all dangers that Odysseus and his men had to overcome on their seemingly endless voyage.
When you are considering the meaning of the first three lines of the poem, however, it is important to understand that the "you" the poet is speaking to is not Odysseus, but rather the reader of the poem. Cavafy is using the journey of Odysseus to Ithaka as a metaphor of the reader's journey through life.
Unlike Odysseus, who was anxious to get back to Ithaka as quickly as he could, the poet cautions the reader to travel slowly, to take time, and to savor the experience of the journey. Cavafy comes back to this thought several times throughout the poem, including in the second and third lines in which he hopes "your journey is a long one, full of adventure, full of discovery." At the beginning of the second stanza he repeats: "Hope your journey is a long one." In the third stanza, he advises the reader, "don't hurry your journey at all" and adds that it is "better if it lasts for years."
Odysseus did not fully appreciate what he found on the way because he was so intent on getting home. In contrast, Cavafy says that Ithaka serves as a destination, nothing more, and that the reader's fulfillment is in the journey itself, not the reaching of the destination. That's why he cautions his readers to go slow and enjoy the adventures, discoveries, pleasures, and joys along the way.
With this in mind, you can understand that Cavafy at the beginning of the poem is addressing his readers as they set out on their voyages through life. He wishes them long, exciting, and fulfilling journeys.

Ithaca—or Ithaka as it's spelled in the poem—is the homeland of Odysseus in The Odyssey. In the ancient Greek poem, Odysseus embarks on a long, exciting journey back to Ithaca after spending seven years on the island of Ogygia, where he was the captive of the beautiful sea-nymph Calypso. In the first three lines of "Ithaka," the speaker expresses the wish that the person he's addressing will enjoy a similar kind of adventure to the one experienced by Odysseus. This could be an actual journey or simply a metaphor for life itself:

As you set out for Ithaka hope your road is a long one, full of adventure, full of discovery.

As well as being full of adventure and discovery, Odysseus's journey was also full of extreme danger, to which the next line in the poem makes reference:

Laistrygonians, Cyclops, angry Poseidon—don’t be afraid of them:

In The Odyssey, the Laestrygonians are a race of giant, man-eating monsters. They eat many of Odysseus's crew and destroy most of his ships by throwing large rocks at them from the top of a cliff. The Cyclops Polyphemus is a fearsome, one-eyed giant who also enjoys snacking on Odysseus's men before he's outwitted by Odysseus himself, who blinds him by ramming a sharpened stake into his eye. And Poseidon, as well as being god of the sea, is also Polyphemus's father and is understandably angry at what Odysseus has done to his son. So he takes a terrible revenge, destroying Odysseus's ship and wiping out all his crewmates through high winds and crashing waves.
What the speaker seems to be saying is that his friend will encounter many problems on his or her journey through life, but they shouldn't be afraid of them. As long as they maintain excitement for the long journey ahead, and as long as they can think clearly and positively, then they should be alright.
https://www.poetryfoundation.org/poems/51296/ithaka-56d22eef917ec

If deputies raid a house looking for evidence but find none, can they still arrest the person? Are there any cases you can recite? If deputies say a crime happened at 3 am, can they have a search warrant by 6 am?

In the United States, a search warrant and arrest warrant authorize different courses of action by police. During the execution of a search warrant, police officers do not have the authority to arrest anyone who happens to be in the building being searched in the absence of probable cause, though—on the basis of reasonable suspicion—can temporarily detain them for purposes for determining identification and other basic facts (see the 1968 case of Terry vs. Ohio). Reasonable suspicion is a lower standard than probable cause.
Further, police must extend a basic level of courtesy to the non-suspect occupants of a building being searched. In the 2009 case United States vs. Thompson, the Supreme Court determined that it was unlawful for authorities to detain a non-suspect occupant of a searched premises for five hours and refuse to permit her to dress.
However, if during the course of the search, officers find probable cause evidence linking one or more occupants of the building being searched to a crime, then they can arrest those persons.
Whether a law enforcement officer can obtain a search warrant in three hours depends on a variety of factors, such as whether sufficient evidence to establish probable cause—which is necessary for a court to issue a search warrant—can be gathered during that time. In most areas in the United States, a judge, magistrate, or court commissioner is either available or can be made available twenty-four hours a day to issue warrants.

Note the answers of William to the comments and questions of Touchstone. What is this purpose? What contrast is shown?

As Duke Frederick’s fool, Touchstone longs for their life at court and mocks everything and everyone he encounters in the Forest of Arden. His character serves to remind the audience of the equally foolish conventions of court life and of the romantic idyllic rustic escape. However, once he meets the country “wench” Audrey, his opinion of the forest begins to change and the audience sees the Romantic in him emerge. In Act V, Scene 1, Touchstone is courting Audrey when her previous suitor, the rustic William, enters. In an aside, Touchstone refers to the other man as also being a fool, and notes that he will not be able to resist making fun of him.
As Touchstone asks apparently simple questions, and William answers them succinctly, Touchstone builds up ammunition to show that William is foolish and unworthy of Audrey. He does this in the style of a lawyer assembling a legal argument, culminating with the assertion that he, not William, should marry Audrey. William's plain answers affirm that he does not understand what Touchstone is up to, and is not a man of words.

TOUCHSTONE: . . . You do love this maid?
WILLIAM: I do, sir.
TOUCHSTONE: . . . Art thou learned?
WILLIAM: No, sir.
TOUCHSTONE: Then learn this of me: to have, is to have; for it is a figure in rhetoric that drink, being poured out of a cup into a glass, by filling the one doth empty the other; for all your writers do consent that ipse is he: now, you are not ipse, for I am he.
WILLIAM: Which he, sir?
TOUCHSTONE: He, sir, that must marry this woman.

Rather than simply tell William to get lost, the fool continues with an elaborate speech, picking up steam and still mocking William, as he pretends that even plain English words need explaining. While he certainly must know that he is not very scary, he threatens to kill William—not once and in just one way, but 350 different ways, and tells him to “tremble and depart.”

TOUCHSTONE: . . . Therefore, you clown, abandon,—which is in the vulgar leave,—the society,—which in the boorish is company,—of this female,—which in the common is woman; which together is, abandon the society of this female, or, clown, thou perishest; or, to thy better understanding, diest; or, to wit I kill thee, make thee away, translate thy life into death, thy liberty into bondage: I will deal in poison with thee, or in bastinado, or in steel; I will bandy with thee in faction; I will o'errun thee with policy; I will kill thee a hundred and fifty ways: therefore tremble and depart.

Audrey, when he finishes, simply adds “Do, good William.” It is clear that she has thrown over her local suitor for the smooth-talking fool.
http://shakespeare.mit.edu/asyoulikeit/asyoulikeit.5.1.html

What motivated English colonization of North America?

It depends on which particular settlement you're referring to. The Jamestown settlement, for example, was primarily a commercial venture. The Virginia Company saw the new colony they established (Jamestown) as an opportunity to generate considerable wealth. Young Englishmen were lured to Jamestown by the prospect of riches, which they hoped would allow them to return home with the wherewithal to lead lives as respectable gentlemen. Jamestown was looked at, then, as a means to an end; it was a short-term project designed to exploit the native natural resources for all they were worth.
Later colonies, such as Plymouth, were established on rather different grounds. In seventeenth-century England, official religious persecution by the authorities led many Protestant dissenters to feel that they needed to seek a new land where they could freely exercise their religion in peace. Because of its very nature, this was a long-term project. And so the Pilgrim Fathers sought to establish a godly kingdom which would endure, acting as an inspiration for countless other Protestant dissenters looking for a haven from intolerance and persecution.

What are some of the biggest challenges facing the planet according to Brief Answers to the Big Questions by Stephen Hawking?

In Brief Answers to Big Questions, Hawking discusses a great number of challenges to the planet and its inhabitants, including the most dangerous threats to our sustained suitability. He describes several global catastrophic risks that could damage mankind on a worldwide scale. He discusses an asteroid impact similar to the proposed impact that wiped out the dinosaurs. His primary worry in this regard seems to be that there is no real way of stopping such an impact. Hawking also discusses the challenge of combating climate change, warning that the release of too much CO2 released into the atmosphere would make our atmosphere unsuitable for human life, and that the amount of CO2 being released is already at dangerous levels. Nuclear war seems to also be of concern. Hawking seems to have accepted that at some point, a nuclear holocaust will devastate if not completely destroy humanity. He also uses an entire section of the book to ponder on whether technology will save or doom us, weighing the pros and cons of artificial intelligence and human augmentation.

How would you make sure that first responders are able to communicate with each other and a command center?

There are many new developments in information technology (IT) that could benefit first responders, particularly in regard to communication. Obviously, first responders make excellent use of telephone systems, but there are more advanced steps to take.
First, you’d want to ensure that there is a consolidated intranet for communication, probably with a central node focused at the responders' base site. That way, all communication could be monitored and rerouted as necessary. Additionally, it would greatly benefit the responders to install mobile hotspot WiFi systems in their vehicles to allow for VoIP calling if there is poor cellular service and to facilitate chat systems like Cisco Jabber. A partner, other than the driver, in each vehicle could maintain written and verbal communication, thereby documenting everything and preventing confusion or allowing for communication when silence is of the essence. There are many options available, especially with the rapid development of IT infrastructure.