(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then a∣c.

(B) Let p ≥ 2. Prove that if 2^p−1 is prime, then p must also be prime.

(Abstract Algebra)

project question:

'Design and build a thrust measurement system for model aircraft engines '

1- Questions

i) sketch

ii) ideas

iii) plan

iv) introduction, background, theory , abstract etc...

I want an abstract about this topic please, not copy-paste from the Internet

Synthesized Shaped Beam Flat Array Antenna for Digital Beam-Forming Radar Applications, Utilizing Printed Technology.

Given the following specification, design a class diagram using PlantUML. To design the class diagram, use abstract, static, package, namespace, association, and generalization on PlantUML

Specification:

• A school has a principal, many students, and many teachers. Each of these persons has a name, birth date, and may borrow and return books. The book class must contain a title, abstract, and when it is available. Teachers and the principal are both paid a salary.
• A school has many playgrounds and rooms. A playground has many swings. Each room has many chairs and doors. Rooms include offices, restrooms, classrooms, and a cafeteria. Each classroom has many computers and desks. Each desk has many rulers.  

in java please

Project 2: The Triangle Class

Problem Description:

Design a class named Triangle that extends GeometricObject. The class contains:

• Three double data fields named side1, side2, and side3 with default values 1.0 to denote three sides of the triangle.

• A no-arg constructor that creates a default triangle.

• A constructor that creates a triangle with the specified side1, side2, and side3.

• The accessor methods for all three data fields.

• A method named getArea() that returns the area of this triangle.

• A method named getPerimeter() that returns the perimeter of this triangle.

• A method named toString() that returns a string description for the triangle.

For the formula to compute the area of a triangle, see Exercise 5.19. The toString() method is implemented as follows:

return "Triangle: side1 = " + side1 + " side2 = " + side2 +   " side3 = " + side3;

Coding: (Copy and Paste Source Code here)

public class TheTriangleClass {

public static void main(String[] args) {

    Triangle triangle = new Triangle(1, 1.5, 1);

    triangle.setColor("yellow");

    triangle.setFilled(true);

    System.out.println(triangle);

    System.out.println("The area is " + triangle.getArea());

    System.out.println("The perimeter is " + triangle.getPerimeter());

    System.out.println(triangle);

}

}

class Triangle extends GeometricObject {

// Implement it (See below for a complete example, the example is for Rectangle)

}

abstract class GeometricObject {
private String color = "white";
private boolean filled;
private java.util.Date dateCreated;

/** Construct a default geometric object */
protected GeometricObject() {
dateCreated = new java.util.Date();
}

/** Construct a geometric object with color and filled value */
protected GeometricObject(String color, boolean filled)
{
dateCreated = new java.util.Date();
this.color = color;
this.filled = filled;
}

/** Return color */
public String getColor()
{
return color;
}

/** Set a new color */
public void setColor(String color)
{
this.color = color;
}

/** Return filled. Since filled is boolean,
29 * the get method is named isFilled */
public boolean isFilled()
{
return filled;
}

/** Set a new filled */
public void setFilled(boolean filled)
{
this.filled = filled;
}

/** Get dateCreated */
public java.util.Date getDateCreated()
{
return dateCreated;
}

@Override
public String toString()
{
return "created on " + dateCreated + "\ncolor: " + color + " and filled: " + filled;
}

/** Abstract method getArea */
public abstract double getArea();

/** Abstract method getPerimeter */
public abstract double getPerimeter();
}

Question based on the business course

24. The United States has a Masculine Orientation when compared to a country like Sweden . Which of the following statements are true

a.The US encourages power, physical strength, and domination Sweden values submission and politeness .

b. The US focuses on results , achievement and competition ; Sweden focuses on modesty , work/life balance ,

and promoting equality.

25. Which of the following are NOT terms used to describe and compare Divergent Cultural Characteristics

a. High context vs. Low context

b.bAtheistic vs. Polytheistic

c. Implicit rule vs Explicit-Rule

d. Long-term vs. Short-term orientation

26. in Uncertainty-Rejecting cultures, such as Japan and Saudi Arabia:

a.Employees are encouraged to question policies and/or regulations

b. Society is resistant to change and seeks to avoid unnecessary risks

c. Freedom of expression is celebrated

d. Few clear rules or regulations exist

c.The US prizes sports, cars, and the military Sweden values furniture, music, and meatballs .

d. The US rewards manliness and winning ; Sweden rewards feminism and beauty

30. When trying to get in touch with a coworker who is out of the office for the day, you should try to:

a. Send a text message to their personal mobile phone during business hours

b. Email them immediately once the work day is over

c. Try your best to reach them by their preferred method of contact

d. Call and leave a detailed voicemail

33. Which of the following groups of words are ONLY CONCRETE subjects ?

a. teamwork , initiative, customer service representative

b. strategy , goal, advertising firm .

c.ethics , competition , challenge

d. coworker , document , supervisor

35. Identity the sentence focus error(s) in the following sentence: The marketing strategy was developed by the CEO of the company.

a. abstract subjects, passive voice, and faulty expletives

b. abstract subjects and faulty expletives

c. abstract subjects and passive voice

d. faulty expletives ONLY

36. Identity the sentence focus error(s) in the following sentence: There are number of reasons why record profits will be earned by Apple in 2019.

a. abstract subjects ONLY

b. passive voice and faulty expletives

c. abstract subjects, passive voice, AND faulty expletives

d. passive voice ONLY

Suzy purchased 2 acres of vacant land in 2018 by paying $4,000 in cash at closing and borrowing $40,000 to be repaid at $8,000 per year for the next 5 years with interest on the unpaid balance at 10%. As part of the purchase agreement, Suzy agreed to let the seller store farm equipment on the land for 2 years (rental value of $1,000 per year). Suzy also pays legal, survey and title abstract fees of $700 on the purchase. In 2019, she paid $1,250 in property tax on the land. In addition, the county paved the road that runs by the land and assessed each taxpayer $1,300 for the paving, which Suzy paid in November 2019. What is Suzy's adjusted basis of the land at the end of 2019?

How is a technical report different from a news report? Mention their differences