4. Verify that the Cartesian product V × W of two vector spaces V and W over (the same field) F can be endowed with a vector space structure over F, namely, (v, w) + (v ′ , w′ ) := (v + v ′ , w + w ′ ) and c · (v, w) := (cv, cw) for all c ∈ F, v, v′ ∈ V , and w, w′ ∈ W. This “product” vector space (V × W, +, ·) is commonly (and more appropriately) denoted as V ⊕ W, called the direct sum of V and W. The Euclidean plane R 2 ≡ R × R is in fact R ⊕ R. (Remark. This notion of direct sum can be extended to the direct sum of finitely many vector spaces V1 ⊕ V2 ⊕ · · · ⊕ Vk in a straightforward way.)

In this program you will read a file specifying a directed graph G as a list of edges. Each edge u →v is listed on one line as u v. The input file simply lists the edges in arbitrary order as pairs of vertices, with each edge on a separate line. The vertices are numbered in order from 1 to the total number of vertices. The program outputs the out-degree sequence for G^SCC in increasing order.

For example for the input below:

2 1

3 2

1 3

1 5

3 4

4 5

6 7

5 6

7 4

3 11

2 8

8 9

10 8

9 10

9 4

9 7

10 11

7 11

6 11

the corresponding output is:

0 1 2 3

You should be able to implement this program to run in linear time (time proportional to the total number of vertices plus the total number of edges in the input graph)

wood-chip manufacturing plant. Persons employed in this plant include: tree cutters, truckers, machine operators, packagers, assembly line workers, secretarial staff, management staff, janitorial staff, marketing and publicity staff, accounting staff and miscellaneous staff. Recently, labor leaders of the plant approached you, as an epidemiologist in the public health center, because they are concerned about what they perceive is an increase in respiratory complaints among employees. Design a cohort study to evaluate their concerns. Would you conduct a prospective or a retrospective study? What outcomes might you be interested in evaluating? Explain the strengths of your chosen study design.

In 2002, Trask et al. published a study showing that a high frequency of HIV transmissions in Lusaka, Zambia occurred between marriage partners. Specifically, they studied a cohort of married couples where, at the beginning of the study, one partner was infected and the other was not. Later, the uninfected partner became infected. If you were doing this study, how could you use phylogenetic methods to determine whether the newly infected individual was likely infected by his/her partner? Briefly describe your study design and results that would support and results that would refute (you can use drawings if you wish) the partner-partner transmission scenario.

For a particular DRAM design the cell capacitance is C,=50fF, Vpp=5 V and V=1.4 V. Each cell represents a capacitive load on the bit line of 2fF. The sense amplifier and other circuitry attached to the bit line has a 20fF. What is the maximum number of cells that can be attached to a bit line while ensuring a minimum bit line signal of 0.1 V? How many bits of row addressing can be used? If the sense amplifier gain is increased by a factor of 5 how many word line address bits can be accommodated.

In recent months, two new stores have opened in town. Each claims to have the best selection for the best price! Use the shopping list below to make a decision about which grocery store you would choose to patron if you were interested in maximizing the number of items you can buy for the least amount of money.

Shopping List:Tide Original High Efficiency Liquid Laundry Detergent, 100 oz;

Bounce Fabric Softener Dryer Sheets, Outdoor Fresh, 240 sheets;

Pantene Pro-V Classic Clean Shampoo, 20.1 fl oz;

Listerine Cool Mint Antiseptic Mouthwash Oral Care And Breath Freshener, 1.5 L;

Olay Moisturizing Face Lotion for Sensitive Skin, 6.0 fl oz;

Opti-Free Pure Moist Contact Solution, 20 fl oz;

Windex Original Glass Cleaner Spray, 23 fl oz;

Febreze Fabric Refresher with Gain Original, 27 oz;

Folgers Gourmet Supreme Dark Roast Ground Coffee, 24.2 oz;

LEGO Creator Mighty Dinosaurs 31058

Find the median of money spent on items ON THE SHOPPING LIST for both Company A and Company B.

Important!: The shopping list only has 10 items; whereas, the entire list has 30 items.

Median cost of items for Company A on the shopping list: (Go to two decimal places):$

Median cost of items for Company B on the shopping list: (Go to two decimal places):$

You have a 200 Ω resistor, a 0.400-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0V and an angular frequency of 250 rad/s.

Parts A, B, C
For this R-L circuit graph v, vR, and vL versus t for t = 0 to t = 50.0 ms. The current is given by i=Icosωt, so v=Vcos(ωt+ϕ).

Part D
What are v, vR, and vL at t = 20.0ms?
Enter your answers numerically separated by commas.

v,vR,vL v , v R , v L = ?, ?, ? V

Part F
What are v, vR, and vL at t = 40.0ms?
Enter your answers numerically separated by commas.

v,vR,vL v , v R , v L = ?, ?, ? V

Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V , i.e., <T(u),T(v)> = <u,v>, ∀u,v ∈ V , is an isomorphism.

Overview

Students will learn how to use block-level <div> elements in HTML and style them with CSS to transform them using various properties such as:

• position
• top, left, right, bottom
• float
• border
• border-radius
• background-color
• etc.

Related Lecture(s)

• Module 2: Lecture #3 - The Box Model & Positioning Elements

Basic Content

1. Create a folder on your local machine in the "csis1430/htdocs" folder called "little-boxes" with the following folder structure:
   • css
   • img
   • js
2. Create an index.html file with multiple (as many as needed, but at least 15) divs
3. Create a style.css file in the css folder
   • Modify the divs using CSS to completely transform them into a cohesive "thing"
   • The "thing" can be anything. Some examples:
     • Houses
     • A scenery
   • See examples from previous students below
4. IMPORTANT NOTE: Do NOT use images in any way. i.e..
   1. No <img> tags
   2. No background-images
   3. etc.
   4. no images
5. Lastly, no tags other than <div> tags are allowed to be used inside the <body> tag.

https://www.youtube.com/watch?v=Rv1bKo3SskY&feature=emb_logo