ENG EK 103 Study Guide - Quiz Guide: Linear Combination, Rotation Matrix, Sinti

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21 Feb 2023

School

Boston University

Department

Engineering Core

Course

ENG EK 103

Professor

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Document Summary

Eng ek 103: computational linear algebra, fall 2022. For these problems, you may use matlab to check your work, but you must show your steps for credit: diagonalize the matrices in part a-d below (i. e. , express in the form ! if possible. By computing powers of ! as ) , we showed that the prediction approaches a steady state regardless of the initial state. In other words, the influence of the initial state wanes as ) increases, and the prediction is governed by the model rather than initial state. Here we examine this by forming an explicit solution for a dynamical system. Suppose in any given election cycle, 80% of those who voted democrat last time will continue to vote democrat, while 90% of republicans will continue to vote republican. Democrats and 10% of republicans switch each election. We can express this system using a probability matrix (also called a markov matrix)

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Hello I need this as soon as possible you must write 250 word of your own nothing copied off of google I will like and follow you see the picture for more information it has the homework on it please need it asap thank you

Tea Party!

Welcome to the Tea Party. You are the host. You will send out invitations to six people in the group below - but only six. Choose your guest list based on who you find most interesting and who you would like to learn more about at the party. You then will write an essay explaining the following:

1. Why did you invite the six members you did? Why not the others?

2. When you sit down at the table, where will you sit everyone - and why will you sit them there? What will be the arrangement of the table?

3. What types of conversations do you expect the group to have? What topics do you expect them to discuss?

1960's

Choose six of the following:

John F. Kennedy Martin Luther King, Jr.

Malcolm X Lyndon Johnson

Ho Chi Minh Richard Nixon

Bobby Kennedy Lee Harvey Oswald

Jack Ruby Nikita Krushchev

Neil Armstrong Muhammad Ali

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*Please refer to the attached file.

You are writing a rough draft for the essay part 1,

This writing practice will focus on

Steps *1 and *2 below:

___________________

FIVE STEPS OF WRITING~*1- Prewrite*2-Draft 3- Revise 4- Edit/Proofread 5- Publish

Expository Essay Part 1

Student Resource

EXPOSITORY ESSAY

– explains, points out

Used in articles, essays, exam questions

- Used to report on research

- Used to share information, give directions

REVIEW:

Elements of Expository Essay:

Thesis

–

Thesis Statement states topic, introduces supporting points

Structure

–

- Organization - often by Cause/Effect, Problem/Solution, Compare/Contrast

- Supporting paragraphs (at least one per supporting point)

- Use of formatting, graphics, and multi-media where appropriate

- Conclusion - relates to thesis and pulls supporting points together

Style

–

- Formal tone - complete sentences; conventional construction and language

- Active voice

Assignment:

Complete the first

two

steps in writing an Expository Essay.

You can use the sample writing prompt on Page 3 or choose a topic based on stories/articles of

your choosing. Page 3 also gives a sample thesis and outline based on the writing prompt. If

writing on your own topic and texts, choose three texts from different genres – e.g., short story,

science fiction, poetry, memoir, informational text, etc.

Step 1)

Prewrite

– Write your thesis statement.

– Determine the structure and organization (e.g., compare/contrast).

– Make an Outline (should include the thesis statement plus a list of

supporting points and a conclusion).

Step 2)

Draft

– Follow your Outline.

– Consider the audience's knowledge of and experience with the topic.

– Give concrete examples (each supporting point should be at least one

paragraph).

– Relate each point back to the thesis statement.

– Draw a conclusion that relates to the thesis statement and ties the

supporting points together.

Expository Essay Part 1

Student Resource

EXPOSITORY ESSAY - SAMPLE THESIS AND OUTLINE

WRITING PROMPT

Compare/contrast the authors' treatments of the theme of

taking

responsibility

in three different genres of text:

Short Story

–"Through the Tunnel,"

Science

Fiction

– "A Sound of Thunder," and

Informational Text

– "Quit blaming; take responsibility."

Thesis

Authors Lessing, Bradbury, and Gitomer, writing in three different textual genres,

each address the theme of taking responsibility by contrasting instances of responsible and

irresponsible behavior and drawing the conclusion of the benefits of taking responsibility.

Supporting paragraphs

– with formatting (subtitles):

1. Short Story

– Lessing ("Through the Tunnel") contrasts Jerry's irresponsible/ responsible

behavior and draws conclusion responsibility is best – Jerry feels better about himself.

- Irresponsible: Jerry tries to get attention, be accepted by other boys; wants to swim

through tunnel before ready (examples from story)

- Responsible: Jerry stops trying to please other boys; adopts his quest; trains and works

to be prepared (examples from story)

- Lessing draws unstated conclusion of benefits of taking responsibility

(contrasts Jerry's feelings before and after quest)

2. Science Fiction

– Bradbury ("A Sound of Thunder") contrasts Time Safari Inc.'s/ Eckels'

responsible/irresponsible behavior and graphically illustrates the devastating results of

irresponsibility.

- Irresponsible: Eckels' uncaring, irresponsible attitude (examples in story)

- Responsible: Time Safari's careful planning and preparation for the hunt

(examples

from story)

- Bradbury ends story showing dramatic impact of being irresponsible, implying the

benefits of responsibility

3. Informational Text

–

Gitomer ("Quit blaming; take responsibility") compares salespeople

with politicians in their tendency to avoid taking responsibility and contrasts that attitude with

suggestions on taking responsibility to achieve success.

- Irresponsible: Salespeople and politicians blame others for their failures

(specific examples from article)

- Responsible: Suggestions on how they can take responsibility by

studying failures and

making them successes (examples in article)

- Gitomer concludes that salespeople (and politicians) can achieve results

they seek by

overcoming obstacles and taking responsibility

Conclusion

Authors Lessing, Bradbury, and Gitomer, writing in three different textual

genres, each address the theme of taking responsibility by contrasting instances of responsible

and irresponsible behavior, concluding that taking responsibility brings the best r

This writing practice will focus on

Steps *1 and *2 below:

___________________

FIVE STEPS OF WRITING ~* 1-Prewrite* 2- Draft 3- Revise\ 4- Edit/Proofread 5- Publish

Expository Essay Part 1

Student Resource

EXPOSITORY ESSAY

– explains, points out

Used in articles, essays, exam questions

- Used to report on research

- Used to share information, give directions

REVIEW:

Elements of Expository Essay:

Thesis

–

Thesis Statement states topic, introduces supporting points

Structure

–

- Organization - often by Cause/Effect, Problem/Solution, Compare/Contrast

- Supporting paragraphs (at least one per supporting point)

- Use of formatting, graphics, and multi-media where appropriate

- Conclusion - relates to thesis and pulls supporting points together

Style

–

- Formal tone - complete sentences; conventional construction and language

- Active voice

Assignment:

Complete the first

two

steps in writing an Expository Essay.

You can use the sample writing prompt on Page 3 or choose a topic based on stories/articles of

your choosing. Page 3 also gives a sample thesis and outline based on the writing prompt. If

writing on your own topic and texts, choose three texts from different genres – e.g., short story,

science fiction, poetry, memoir, informational text, etc.

Step 1)

Prewrite

– Write your thesis statement.

– Determine the structure and organization (e.g., compare/contrast).

– Make an Outline (should include the thesis statement plus a list of

supporting points and a conclusion).

Step 2)

Draft

– Follow your Outline.

– Consider the audience's knowledge of and experience with the topic.

– Give concrete examples (each supporting point should be at least one

paragraph).

– Relate each point back to the thesis statement.

– Draw a conclusion that relates to the thesis statement and ties the

supporting points together.

Expository Essay Part 1

Student Resource

EXPOSITORY ESSAY - SAMPLE THESIS AND OUTLINE

WRITING PROMPT

Compare/contrast the authors' treatments of the theme of

taking

responsibility

in three different genres of text:

Short Story

–"Through the Tunnel,"

Science

Fiction

– "A Sound of Thunder," and

Informational Text

– "Quit blaming; take responsibility."

Thesis

Authors Lessing, Bradbury, and Gitomer, writing in three different textual genres,

each address the theme of taking responsibility by contrasting instances of responsible and

irresponsible behavior and drawing the conclusion of the benefits of taking responsibility.

Supporting paragraphs

– with formatting (subtitles):

1. Short Story

– Lessing ("Through the Tunnel") contrasts Jerry's irresponsible/ responsible

behavior and draws conclusion responsibility is best – Jerry feels better about himself.

- Irresponsible: Jerry tries to get attention, be accepted by other boys; wants to swim

through tunnel before ready (examples from story)

- Responsible: Jerry stops trying to please other boys; adopts his quest; trains and works

to be prepared (examples from story)

- Lessing draws unstated conclusion of benefits of taking responsibility

(contrasts Jerry's feelings before and after quest)

2. Science Fiction

– Bradbury ("A Sound of Thunder") contrasts Time Safari Inc.'s/ Eckels'

responsible/irresponsible behavior and graphically illustrates the devastating results of

irresponsibility.

- Irresponsible: Eckels' uncaring, irresponsible attitude (examples in story)

- Responsible: Time Safari's careful planning and preparation for the hunt

(examples

from story)

- Bradbury ends story showing dramatic impact of being irresponsible, implying the

benefits of responsibility

3. Informational Text

–

Gitomer ("Quit blaming; take responsibility") compares salespeople

with politicians in their tendency to avoid taking responsibility and contrasts that attitude with

suggestions on taking responsibility to achieve success.

- Irresponsible: Salespeople and politicians blame others for their failures

(specific examples from article)

- Responsible: Suggestions on how they can take responsibility by

studying failures and

making them successes (examples in article)

- Gitomer concludes that salespeople (and politicians) can achieve results

they seek by

overcoming obstacles and taking responsibility

Conclusion

Authors Lessing, Bradbury, and Gitomer, writing in three different textual

genres, each address the theme of taking responsibility by contrasting instances of responsible

and irresponsible behavior, concluding that taking responsibility brings the best r

isaiahh223g

Saturn V First-Stage Structural Analysis The first stage of the Saturn V (also called the S-IC) provided thrust to lift the second stage, third stage, and payload to an altitude of about 100km within the first 150 seconds of flight, at which point it experienced a maximum acceleration of 38𝑚/𝑠2 . The first stage structure (the shell around the propellant tanks) transmitted the force produced by the engines to the upper stages through its outer skin. This skin was composed of 2219-T87 aluminum, which has a Young's modulus of 73.1GPa, a yield strength of 390MPa, a density of 2840 𝑘𝑔/𝑚3 , and a thermal expansion coefficient of 22 ∗ 10-6𝐾-1 . We will perform an analysis of the S-IC structure and the loads it carried through a series of scenarios. The exception is for Part 5, which must be done by hand as it requires significant drawing and only uses symbolic variables, no numerical calculations. I also recommend setting up the equations for Part 4 by hand and then using the .m file to perform the actual computations.

Part 1:

The S-IC stage shell was required to support the load of the second stage, third stage, instrument unit, and Apollo spacecraft modules, both on the pad and during launch. The maximum mass it had to support was when the fully-fueled vehicle was sitting on the pad, and the maximum acceleration it experienced was immediately before stage burnout (when the S-IC was empty but all the other stages were full). Assume the S-IC tank structure is a smooth cylinder with an outer diameter of 10 meters, a thickness of 5.5 mm, and a height of 41 meters when nothing is mounted on top of it. The empty mass of everything above the stage is 9.7 ∗ 104 𝑘𝑔, and the mass of everything above the stage is 2.9 ∗ 106 𝑘𝑔 when fully fueled.

Find:

• How much the stage shrinks when the empty stages are placed atop the S-IC

• How much the stage shrinks when the vehicle is fully fueled

• How much the stage shrinks under full acceleration

• The average axial stress experienced in each of these three cases

• The factor of safety in each of these three cases Ignore the mass of the S-IC structure itself and propellant; all we care about is how the tank has to deal with supporting the masses above it.

Part 2:

In reality, the stage did not have a uniform cross section; it was composed of steps of decreasing thickness toward the top of the S-IC, to save structural mass. Suppose the tank wall thickness decreased from 6.5 mm at the bottom to 4.3 mm at the top in eight steps of equal height. Each of the eight "rings" would have a constant wall thickness, the same height as the other rings, and the total height of the stage would still be 41 meters. Repeat the first three bullet points from Part 1, to find how much the stage will contract with the stepped cross sections instead of the uniform. Additionally, find the mass savings by constructing the tank in this manner.

Part 3:

If the 41m height measurement given in Part 1 was taken at an ambient temperature of 25C, how much would the entire S-IC shrink due to thermal contraction (with no load atop the stage) at an operating temperature of -100C? You may choose either the uniform or stepped cross-section configuration from Part 1 or Part 2 to solve this problem, but there is one optimal solution within the scope of this project. Explain which option you chose and why.

Part 4: Consider the planar truss section shown. Suppose four of these held the S-IC stage upright on the mobile launch platform. If the weight each had to support was 6.9MN (labeled F in the diagram), find the reaction forces at joints B and C (a total of three quantities) and the internal forces in the rods AB, AC, and BC. You may assume that the load is balanced and there is no moment about point A. ABC is an equilateral triangle. Be sure to include your sanity check of the static equilibrium of the whole structure. Briefly describe why the analysis would be complicated by making point C a fixed reaction joint like point B instead of a roller joint.

Part 5: Draw a SMD for the transverse axis of the S-IC using symbolic values (no numbers). The diagram should reflect: 1. A constant, even transverse pressure the vehicle experiences due to wind at the pad (note that this must include the wind pressure experienced by the upper stages, collectively referred to as 𝑃𝑊). 2. The fixed base of the vehicle on the pad. 3. A fueling arm located at 𝑙/2 from the base of the rocket that exerts a load 𝑃𝑓 in a direction counter to the wind. 𝑃𝑓 is not large enough to counteract all the shear experienced by the stage at station 𝑙/2. 07 Apr 2022 Hint: for this problem, continue drawing the SMD along the X axis, with the fixed base at the bottom of the rocket.

Part 6:

The LOX tank bottom is hemispherical, with a total tank height of 19.5 meters tip-to-tip. Suppose the tank were pressurized to 151 kPa and contained LOX with a density of 1141 𝑘𝑔/𝑚3 . Use the Bernoulli equation to find the pressure at the bottom of the tank (at surface gravity) and the thin wall pressure vessel stress experienced by the bottom of the hemispherical tank bottom. At burnout, the tank was empty of liquid oxygen but still under gaseous pressure of 151 kPa. Find the longitudinal and circumferential stresses about the central cylindrical section of the tank. For this part, ignore acceleration, axial forces, thermal deformation, ambient pressure, etc.

Part 7: Even if composite materials (like carbon fiber) had been widely available in the 1960s, give three reasons why they would be less desirable for an application like the S-IC stage than aluminum or titanium

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ENG EK 103 Study Guide - Quiz Guide: Linear Combination, Rotation Matrix, Sinti

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