Other Questions & Answers

Amby Burfoot, an editor for a magazine, has many reasons for running. Which of the following is NOT on her list of reasons to run? (A) weight loss (B) recreation (C) high pay (D) stress relief

A relation \( \mathcal{R} \) is defined by \( \mathcal{R}=\left\{(x, y): 1<x^{2}-y^{2}<5, x, y \in \mathcal{Z}\right. \). (a) List down the Domain and Range of \( \mathcal{R} \). (b) list down all the elements of \( \mathcal{R} \). (c) \( \mathcal{R} \) an equivalence relation?

Line fishing: fish caught using a fishing or by using a fishing line. Recreation: an activity done for relaxation, fun and/or sport. Geelbeck, red and white steenbras, rockcod, red stumpnose, carpenter musselcracker, shell mussel and calamari ... these are some of the widel consumed line fish species of which stock are at dangerously low levels. An alarming \( 67 \% \) of our top 27 recreational line fish species (that is, they ar caught in the inshore zone between the depths of 5 metres and 130 metres) have been classified as 'collapsed'. Six out of the ten of our most important commercial line fish species fall well belov critical stock levels in the Western Cape - where the bulk of national line fist catches are made. Stocks of kingklip, prawns, sole, shrimps and oysters are heading for depletion while snoek, dorado, yellowtail and sardines are still in adequate supply. In 2004 the South African Sustained Seafood Initiative (SASSI) informe consumers, by giving fish in large supply: a green status (for example, the dorado) those fish species that are in danger of being destroyed: the orange status (fo example, kingklip) and those fish species that are almost destroyed, a red statu (for example, red and white steenbras) the consumer can make more responsible choices. [Source: Adapted from Via Afrika, Social Sciences, Grade 9] 4.1.1. Explain what is meant by unsustainable fishing. 4.1.2. Mention TWO impacts of overfishing 4.1.3. Refer to the last paragraph of the text above. the line fish they are eating. ensure that the stock of orange and red status line-fish are not depleted (complete destroved).

Her the topology \( T=\{\phi, X,\{a),\{a, b),(a, c, d),\{a, b, c, d),\{a, b, e\}\} \) on Given a subset \( A=\{c, d, e\} \), Find; Derived set of \( A \). Relative topology on \( A \).

h) Define the lincar transformation \( T: \mathbb{R}^{4} \rightarrow \mathbb{R}^{3} \) by \( T\left(\left[\begin{array}{l}d \\ b \\ c \\ d\end{array}\right]\right)=\left(\left[\begin{array}{l}a+b \\ b-c \\ a+d\end{array}\right]\right) \) i. Find a basis for the null space of \( T \) and its dimension ii. Describe the Range of \( T \) iii. Find a basis for the range of \( T \) and its dimension

- Show that A and B are not similar matrices. \[ A=\left[\begin{array}{ll}4 & 1 \\ 3 & 1\end{array}\right] \cap B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \]

2. Изучить социальные и экономические предпосьглки для написания учебника. 3. Изучить какие труды древних учёньтх использовал Магницкий для составления своего учебника.

h) Define the linear transformation \( T: \mathbb{R}^{4} \rightarrow \mathbb{R}^{3} \) by \( T\left(\left[\begin{array}{l}a \\ b \\ c \\ d\end{array}\right]\right)=\left(\left[\begin{array}{l}a+b \\ b-c \\ a+d\end{array}\right]\right) \) i. Find a basis for the null space of \( T \) and its dimension ii. Describe the Range of \( T \) iii. Find a basis for the range of \( T \) and its dimension

QUESTION ONE ( 30 MARKS) a) Let \( X=(a, b) \). list down all the possible topologies on \( x \).

1. Attempt quescion one and any orfrer fwo questions QUESTION ONE ( 30 MARKS) a) Let \( X=(0, b\} \). list down all the possible topologies on \( X \). b) Show that \( T=\{\phi,\{1\},\{3,4\},\{1,3,4\},\{2,3,4\}\} \) is not topology on \( X=\{1,2,3,4\} \). (2 Marks) c) Distinguish between finer and coarser topology.