I would like to write about the Franciscan Order and then briefly describe two other monastic movements, while showing how Franciscans were and are different. For example, some emphasize the eremitical aspect of praying, fasting, meditating, while others emphasize missionary, pastoral, and educational efforts.

An excellent and accessible source for the life of St. Francis, founder of the Franciscans, is Paul Sabatier's The Life of St. Francis of Assisi. It was one of the first books to apply modern, objective techniques of scholarship to a Roman Catholic saint.
The Franciscan order is most notable for its vows of poverty. As Sabatier outlines, Francis did not want to found a typical monastic order in which the brothers would own and live in a monastery. Instead, he envisioned them as a mendicant order, one that would raise all its funds through begging. This would be successful, St. Francis thought, because the needs of his brothers would be extremely simple—bare feet, rough, ragged robes, just enough food to survive, and rough huts for housing. Begging and owning nothing would help reinforce their humility. It would also emphasis the reality that all provision comes from God. This was a literal living out of the line in the Lord's Prayer, "give me this day my daily bread."
Francis envisioned his followers living in joyful poverty and did not intend for them to be focused on their sin (he himself was given to flagellation to rid himself of material desires but later apologized to his body for what he had done to it). He himself found joy in a poor life and wanted his followers to experience and express the beauty and joy of God's creation. He also wanted his followers to serve the poorest of the poor with joy and gratitude. He was notable himself for his charity toward lepers, a feared and despised group in his society.
As Francis was dying, he did agree to allow the Franciscans to become more like a typical monastic order, though he had resisted such a move earlier. While there has always been a tension between the order's vows of poverty and communal ownership of property, the severity of Francis's vision has been relaxed. The monks do live in typical monasteries. They still, however, emphasize simple, humble living, as well as serving the poor and blessing the animals and creation. The current pope, St. Francis, exemplifies many ideals of the Franciscans. For details of some of the difficulties living in a order based on charity in times past, you might look at the book Galileo's Daughter, by Dava Sobel. 
The Carthusians are an eremetical order you might focus on to contrast with the Franciscans. The Carthusians are contemplative brothers who live together in a monastery, focusing on lives of prayer, solitude, and silence. 
The Jesuits, an order founded in the sixteenth century, are known for their global missionary work and their emphasis on education.

What would be a critical appreciation of "To a Skylark" by Percy Bysshe Shelley?

"To a Skylark" is a poem written by Percy Bysshe Shelley in June 1820. It consists of twenty-one five-line stanzas. The stanzas each consist of four lines of iambic trimeter followed by a line of iambic hexameter. The rhythm generally follows the metrical scheme, with the more common variations including acephalous lines and spondaic substitutions. The rhyme scheme is ABABB. The majority of the lines are end-stopped with prominent rhyme words—some monosyllabic with long vowels but a few with feminine rhymes. The relatively regular rhythm, the use of trimeter, and the end-stopped lines give the intended effect of a song, mimicking the song of the skylark.
In the poem, a first-person narrator uses the rhetorical technique of apostrophe, personifying the bird and talking to it as though it were a person. As is typical of Romantic poetry, the narrator sees the bird as an emblem of pure joy that is "better than all treasures / That in books are found."
The poet rather plaintively asks the bird to teach him the joy that appears in the song and suggests that the ideal poem reflect such teachings, thus imitating the pure joy of the skylark song.

Before tackling this question, it helps to understand what a critical appreciation is. A critical appreciation is a knowledgeable evaluation of a piece of literature or poetry. For instance, the reader must have enough relevant knowledge about the particular piece in order to construct an informed opinion about it. It's worth noting that a critical appreciation can like or dislike the piece of literature being examined; the important thing is to know enough about the work to give good reasons for why you like or dislike it. 
With this knowledge in mind, let's look at "To a Skylark" by Percy Bysshe Shelley. Your critical appreciation will depend on the particular context from which you approach the poem, and also on what you like or dislike about it. It's still possible to provide some examples, though. For instance, you could say you like the poem because it skillfully uses a skylark as a metaphorical representation of the natural world. Conversely, you could say you dislike the poem because its archaic language makes it difficult to read and comprehend. Whatever the case, you'll need to back up your particular opinion by offering a careful and insightful analysis of the poetic characteristic you're discussing. Your opinion does not necessarily matter, as long as you back it up with a sound evaluation of the work in question. 
https://www.poetryfoundation.org/poems/45146/to-a-skylark

College Algebra, Chapter 1, 1.4, Section 1.4, Problem 16

Evaluate the expression $(2 + 5i) + (4 - 6i)$ in the form of $a + bi$.


$
\begin{equation}
\begin{aligned}
&= (2 + 5i) + (4 - 6i)\\
\\
&= (2 + 4) + (5 - 6)i\\
\\
&= 6 - i
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 50

Determine $\displaystyle \int^5_0 f(x) dx$ if
$
f(x) = \left\{
\begin{array}{c}
3 & \text{for} & x < 3\\
x & \text{for} & x \ge 3
\end{array}\right.
$


$
\begin{equation}
\begin{aligned}
\int^5_0 f(x) dx &= \int^3_0 3 dx + \int^5_3 x dx\\
\\
\int^5_0 f(x) dx &= (b-a) + \frac{b^2-a^2}{2}\\
\\
\int^5_0 f(x) dx &= 3(3-0) + \frac{(5)^2-(3)^2}{2}\\
\\
\int^5_0 f(x) dx &= 9+ \frac{25-9}{2}\\
\\
\int^5_0 f(x) dx &= 9 + \frac{16}{2}\\
\\
\int^5_0 f(x) dx &= 9+8\\
\\
\int^5_0 f(x) dx &= 17
\end{aligned}
\end{equation}
$

What are the character traits of the characters in The Pearl?

The protagonist of The Pearl, Kino, is a traditional hard-working man who takes great pride in his dignity and unwillingness to give in. He has tremendous love for his wife and child, which strongly motivates him to continue his grueling work. After finding the titular pearl, his ambitions skyrocket, and he becomes obsessed with the idea of freedom from oppression.
Juana, Kino's wife, holds a significant faith in religion. She prays for good fortune, and once Kino discovers the pearl, she begins to believe that the pear holds evil powers. She is a headstrong individual, though she often compromises her own beliefs or ideas in favor of Kino's.
Coyotito is an infant and consequently has few noteworthy traits. Instead, he serves as a plot device; when he is stung by a scorpion, Kino becomes obsessed with the idea of acquiring enough money to send him to the proper doctor, and the plot is thus set in motion.
Juan Thomas is Kino's brother who remains an influential and supporting figure for Kino. A man with strong family values, he becomes concerned when Kino finds the pearl. He hopes for the best for Kino and his own family.
The doctor Kino asks to help Coyotito is a European colonial who feels dissatisfied with his current lifestyle. An arrogant man who thinks he deserves better than he has, he shows his greed when agreeing to help the infant only after learning about the pearl.

Summarize the causes and effects of the Indian Rebellion of 1857.

Causes of the 1857 Rebellion.
By the 1850s, much of India was ruled by the East India Company, a private company consisting of British merchants which had first established its presence in the 1600s. To maintain its authority in India and to protect its economic interests, the East India Company employed large private armies, consisting of native Indians. By 1856, the company employed over 300,000 Indians, many of which were called Sepoys (infantrymen). Around three-fourths of these Sepoys were Hindus while the remaining one-fourth consisted of Muslims.
While the Sepoys were ruled by British officers, the two groups were very different. The British struggled to cope with the intense Indian heat while the Sepoys had a reputation for their strength and skill in combat. There were religious differences, too: the Sepoys followed their religions very carefully, with the Hindus refusing to eat beef and the Muslims refusing to eat pork.
This fact may seem unimportant but, in 1848, Lord James Dalhousie, became the the governor-general of the East India Company and his policy towards the Indians was often harsh and unforgiving. He annexed even more Indian territory for the company, for example, and forced Indian tenant farmers to pay taxes to their British overlords. The most dramatic of his changes, however, came in 1857 when Dalhousie issued a new rifle to the soldiers of his Sepoy army. This rifle was very different to previous models and required the use of animal fat to aid the cartridge as it slid down the barrel of the gun. As devout Hindus and Muslims, the Sepoys refused to grease the barrel with pork or beef fat, as required, and felt insulted by the British. Despite British reassurance that they would not have to, the Sepoys became deeply suspicious and this led to the rebellion which began at an outpost near Delhi in April of 1857. 
Effects of the 1857 Rebellion.
The British retaliated with extreme violence. They captured random Indians, tortured and murdered them. Captured rebels suffered a similar fate: they were tied to a cannon and blasted into hundreds of pieces. At a trading post called Cawnpore, the British looted the town and committed widespread rape and murder.
The Rebellion lasted for over one year and, in 1858, the British were finally able to recapture Delhi and restore order. The British adopted a policy of reconciliation: Queen Victoria pardoned many of the rebels and respect was shown towards the Hindu and Muslim religions. Most importantly of all, the East India Company was abolished and Indian affairs were directly controlled through a specially-appointed governor.

What does the poet hear in his deep heart core?

What the speaker hears is the call of Innisfree and the simple life lived close to nature that it represents. The speaker is profoundly dissatisfied with urban life, which is somehow less real, less authentic than the isolated existence out in the wilderness that he craves. Even in the midst of all the hustle and bustle of the city, the speaker can still hear the call of the wild, feeling it deep within the very depths of his soul. His previous experience of life on the lake isle has clearly had a profound effect upon him, so much so that he has been changed forever by his brief taste of the simple life and its equally simple pleasures.
Though forced to return to the city, the speaker knows that he cannot ignore the insistent call of Innisfree for very long. The remote, rugged landscape has entered his soul, and there it shall remain forever, insistently calling upon the speaker at regular intervals to renew his almost mystical connection with the soil of this most blessed plot of earth.

The speaker in Yeats's poem has been to Innisfree before, and he announces his intention to return. "In the deep heart's core" he hears, even while standing on the roadways and pavements of an urban center, the sounds of Nature that fill the air at Innisfree. In his memory and imagination, the speaker hears the quiet lapping of small waves along the lakeshore that are a constant sound there. He longs to return to hear the waves and the peace that it offers, along with the sound of bees humming in the glade, crickets singing in the morning, and linnets flapping their wings in the evening. The memories of all these peaceful sounds stay with the speaker and inspire him to return to Innisfree and build himself a home.