Discuss energy conservation. What is a radiation source? Describe the uses of radioactive sources within medicine. Discuss half-life.

(Generally, multipart questions are split into different questions and each is posted separately. I will answer some of the questions and provide hints for the rest).
Energy Conservation: This term is most commonly used in reference to the saving of energy or energy sources. When we talk of carpooling or the use of public transport, we are talking about conserving the sources of energy (generally fossil fuels). Similarly, when we talk about using energy-efficient devices, we are referring to the conservation of electrical energy, which in turn will minimize the combustion of fossil fuel in the thermal power plants (this assumption is valid since most electrical energy is generated through the combustion of fossil fuels). Energy conservation is necessary for a number of reasons:
1) Fossil fuels, our most important source of energy, are limited in quantity and will likely run out soon.
2) Fossil fuel combustion generates greenhouse gases, which, in turn, are the reason for global warming.
3) Fossil fuels are not uniformly distributed geographically, and this causes the dependence of nations on a few nations rich in fossil fuels.
Energy conservation will not only minimize global warming, it will also prolong the availability of fossil fuels and minimize the dependence of nations on countries rich in fossil fuels. Efforts are underway at the global level to counter the growing risk of global warming, and one of the key steps is the reduction in the greenhouse gas emissions through the decreased use of fossil fuels. Energy conservation can also help in those efforts by reducing the energy requirements. Use of public transport, energy-efficient devices, development of green buildings, and so on are all energy conservation efforts. An example of an energy efficient device is a LED lamp. It uses less electricity when compared to an incandescent lamp.
Think of a large number of similar examples that can result in energy conservation.
Radiation source: This is simply a source of radiation. Some day-to-day examples of radiation sources include cellphones, X-rays, FM or AM radios, garage-door openers, microwave ovens, and so on. Radiation sources may generate either ionizing or nonionizing radiations. Ionizing radiation, such as gamma rays, may be hazardous to our body. Note that radiation sources can be natural or man-made. Some forms of natural radiation include cosmic radiation, terrestrial radiation from rocks containing radioactive minerals, and so on. Man-made radiation sources may be present in industries, hospitals, nuclear reactors, and so on.
Radiation sources can be beneficially used in medicinal science. The X-ray machine is very commonly used by dentists and hospitals. This machine is a source of X-rays. This equipment is used to locate bone fractures, tooth defects, and so on. Radioisotopes are used for radiation therapy of cancer patients. Similarly, radioactive iodine may be used to treat thyroid problems.
Half-life refers to the amount of time in which a radioactive substance reduces to half of its original amount. For example, uranium-238 has a half-life of about 4.5 billion years. This means that if we start with 1 kg of uranium-238, after about 4.5 billion years, we will be left with around 500 grams of it. One of the most common uses of the half-life concept is in the carbon dating of organic materials.
Hope this helps.

What happened after the trail of tears

When the Cherokee were forcibly resettled in the territory of Oklahoma after the Trail of Tears, their nation faced a period of extreme turmoil. Major Ridge, his son, and other Cherokee signers of the Treaty of New Echota were blamed for the deaths of the 4,000 Cherokee that perished on the Trail of Tears. They were executed by their tribesmen under the Cherokee Blood Law. What followed was a wave of power struggles and violence within the nation. Nearly the entire leadership of the Cherokee was killed or deposed during the years that followed. In short, the Cherokee descended into a civil war that lasted nearly thirty years.
Furthermore, the Cherokee initially had trouble adjusting to life in Oklahoma. In Georgia they had been successful farmers. When they arrived in Oklahoma they did not have the infrastructure in place or the tools to immediately begin farming. As a result, they had to resort to hunting and gathering, a lifestyle they were not used to. Unfortunately, these methods could not provide enough food for the entire population, and many starved. Eventually, and with great difficulty, the Cherokee adjusted to life in the West. Their population ultimately rebounded, and today they are one of the largest Native American tribes in the country.

Careful measurement of the electric field at the surface of a black box indicates that the net outward electric flux through the surface of the box is 6.0 kN⋅m^2/C. What is the net charge inside the box? If the net outward electric flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Explain your answer.

Use Gauss's law relate the electric flux with the charge enclosed in the box. Since the electric flux is directly proportional to the net amount of enclosed charge in the box, if the flux is zero, so is the net amount of charge. Keep in mind there may may equal amount of positive and negative charge.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

Explain how water and glucose can diffuse across a plasma membrane?

Diffusion is a type of passive transport. The cell doesn't have to invest energy to allow the molecules to pass through the plasma membrane.
The plasma membrane is composed of a phospholipid bi-layer. Its hydrophilic and polar "heads" point towards the extracellular environment on the outside of the cell, and towards the cytoplasm on the inside of the cell. Its nonpolar hydrophobic tails are aligned on the inner surface of the membrane. There are proteins embedded in the cell membrane that can serve as transport proteins.
The plasma membrane is selectively permeable which means only certain substances may pass through the cell membrane. These vital substances must be able to enter and leave a cell in order for it to stay alive.
Osmosis is the passage of water across the plasma membrane by diffusion. There must be a region of higher concentration of water on one side of the membrane relative to the other. Aquaporins are channel proteins that help increase the amount of water molecules that can diffuse across the membrane. That is because they have a hydrophilic channel that molecules like water can use as a tunnel through the membrane. Hydrophilic molecules like water do not cross the membrane easily on their own.
Cells need glucose to carry out cellular respiration. If there is a higher concentration of glucose outside the membrane relative to inside the cell, glucose will enter the cell when carrier proteins shuttle the molecules across. Glucose is too large of a molecule to enter a cell unassisted. This is known as facilitated diffusion and does not rely on an additional input of energy from the cell. The difference in concentration from high to low is a concentration gradient that provides the energy for this process to occur. 
The link I provided has details about facilitated diffusion-see number 2 with an excellent diagram, and osmosis-see number 3 in the article.
 
 

How does the author use action, setting, and dialogue to convey the theme that things are not always as they appear to be in A Very Old Man with Enormous Wings?

The author uses elements of the literary genre magical realism to convey that things are not always what they appear to be. Using this approach, Garcia Marquez combines the mundane with the magical to create a world that is both real and unreal.
The setting of the story contributes to the magical realism of the story. Even the opening line contains aspects of magical realism:

On the third day of rain they had killed so many crabs inside the house that Pelayo had to cross his drenched courtyard and throw them into the sea, because the newborn child had a temperature all night and they thought it was due to the stench.

Pelayo's house has strange qualities, as it is inundated with crabs. Pelayo and his wife, Elisenda, also bizarrely believe that their child has taken sick because of the smell of the crabs. While the story contains realistic elements, such as the house by the sea and the sick child, the author also interjects oddities and fantastic elements that upend this reality and suggest that things are not always what they seem.
Several elements of the plot also contain a sense of unreality. For example, the angel cascades to the ground dressed as a ragpicker. Shortly after he arrives, the crowd becomes so big that Pelayo's courtyard is crammed with people. He has to call troops with fixed bayonets. Then, an even more bizarre event occurs:

A traveling carnival arrived with a flying acrobat who buzzed over the crowd several times, but no one paid any attention to him because his wings were not those of an angel but, rather, those of a sidereal bat.

The acrobat in the circus inexplicably has the wings of a bat, but no one even remarks on him because they are concentrated on the strange angel. Later, a woman who has been changed into a spider for having disobeyed her parents also arrives in the traveling show in town. These events mix the real and the fantastic.
The dialogue is also unreal at times. For example, Pelayo and Elisenda's neighbor tells them the following about the strange creature who has fallen by their house: "He’s an angel. . . . He must have been coming for the child, but the poor fellow is so old that the rain knocked him down.” Her remarks are clearly fantastic in nature, but the neighbor is convinced of her beliefs. As the story's setting, plot, and dialogue contain elements of fantasy, the reader is not that surprised when the creature flies away at the end of the story because the author conveys throughout the story that things are not what they seem.

Is Hirschi's (1969) social control theory compatible with Gottfredson and Hirschi's (1990) general theory of crime? Why or why not?

I would argue that these two theories are compatible based on a simple analysis of both.
In essence, Hirschi's social control theory states that societal bonds are the mechanism that prevents people from pursuing the rewards offered by a life of crime. These bonds consist of attachment (emotional connections that we share with people), the commitments that we make to building and sustaining relationships with others, our involvement with work-related and social activities, and our beliefs in right and wrong. When combined, according to social control theory, these factors keep members of society in check.
According to A General Theory of Crime (1990), crime is the result of a blend of opportunity and low self-esteem. An unstable or difficult childhood creates a breeding ground for the development of criminal tendencies, according to this theory.
From a sociological perspective, it is evident that if one has a bad childhood, one is less likely to find it easy to form the types of social bonds described by social control theory. Without these social bonds, according to Hirschi, it would be easier to cast away moral scruples and enter a life of crime.
https://www.britannica.com/biography/Travis-Hirschi

Hirschi's (1969) social control theory posits that people who are delinquents did not form social bonds to society consisting of attachment, belief, commitment, and involvement. Following a Hobbesian viewpoint, Hirschi believes that all humans are capable of committing crimes and that conformity, rather than delinquency, has to be explained. Through the process of socialization, he believes that people form bonds with society, which includes attachment—the link between people and society. Other elements of social bonds include commitment—the time and energy or investment that someone has made in societal institutions. For example, someone who has earned a college degree might be less likely to violate societal norms. Involvement is the third aspect of social bonds, as people who have more structured time that connects them to others are less likely to commit crimes. Belief refers to the degree to which people believe in social norms and are therefore more likely to follow them.
Gottfredson and Hirschi's (1990) general theory of crime postulates that people's degree of self-control explains a person's likelihood to commit or refrain from crime (see the link below for additional information). When a person with the propensity to commit crimes encounters the opportunity to commit a crime, they are more likely to do so. The researchers believe that children raised in situations in which they are not well monitored by adults, in which they are not attached to their parents, and in which the parents encourage criminal behavior, will develop less self-control. People with this orientation are often focused on the present and want to gain rewards without work.
These two theories are to some degree incompatible. Hirschi's (1969) social control theory posits that parents do not need to have direct control over their children but can exercise a kind of indirect control. From this early theory, it follows that even if parents are not present, they can exercise a form of psychological control over their children. However, Hirschi abandoned this idea in the later general theory of crime that he developed with Gottfredson in 1990. The general theory of crime states that parents must monitor their children directly so that the children develop self-control and an orientation for eventual rather than immediate results. The earlier theory states that children can develop some of this connection and self-control on their own while the parents exercise indirect control, while the later theory states that parents must be present and actively instilling values and practices of self-control in their children to encourage law-abiding behavior.
Source:
Wiatrowski, M.D., Griswold, D.B., & Roberts, M.K. "Social Control Theory and Delinquency." American Sociological Review Vol. 46, No. 5 (Oct., 1981), pp. 525-541 Published by: American Sociological Association DOI: 10.2307/2094936.
https://oxfordre.com/criminology/view/10.1093/acrefore/9780190264079.001.0001/acrefore-9780190264079-e-252

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 80

Suppose that one Canadian dollar was worth $1. 0573$ U.S. dollar at a certain time.

a.) Find a function $f$ that gives the U.S. dollar value $f(x)$ of $x$ Canadian dollars.

b.) Find $f^{-1}$. What does $f^{-1}$ represent?

c.) How much Canadian money would $\$ 12,250$ in U.S. currency be worth?


a.) If 1 Canadian dollar = $1.0573$ U.S. dollar, then

$f(x) = 1.0573 x$

b.) To find $f^{-1}$, set $y = f(x)$


$
\begin{equation}
\begin{aligned}

y =& 1.0573 x
&& \text{Solve for $x$, divide } 1.0573
\\
\\
x =& \frac{y}{1.0573}
&& \text{Interchange $x$ and $y$}
\\
\\
y =& \frac{x}{1.0573}
&&

\end{aligned}
\end{equation}
$


Thus, $\displaystyle f^{-1} (x) = \frac{x}{1.0573}$.

If $f(x)$ represents the exchange rate of Canadian to U.S. dollar, then $f^{-1} (x)$ represents the exchange rate of U.S. dollar to Canadian dollar.

c.) If $x = \$12,250 $ U.S. dollar

then its equivalent Canadian dollar is..

$\displaystyle \frac{12,250}{1.0573} = 11,586.16$