人工育教貝三弟張四第日十二月二十年申庚播夏
WAH KIU YAT PO 日僑手
1981
歷史
1981
Argand viagram of cube roots of -81.
中學會考試題預習專欄
(c) The fourth routs of
-2-2√31
中學會考試題預習專欄
Let z
-2-2√31
16cis(360n+240°)
(+*)
(+)
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[2acis(360n°+240o)]
Add.Maths (16)
where n
0
when n
14402,
2cis600.
when n
1
附加數
C. Y.
Shum
MILL & DALE PRESS LTD.
Solutions to Exercise
,(a) iz2+52-1 - 0
Using the formula for solving quadratic
equations:
-b±√b-4ac
2a
-5±√52-4(1)(−1)"
ஆருர் -ஆறு
-51/21
21 (5±√21)1
(35±√21
24(2)(4)
2(2)
(~3±41) i
Ans.
(a) The fifth roots of unity:
1
1401
cis(360n
360n
cis
cis72n
when
when n
2eis(90n+60°)
when n
where 207
2cis 1500
2,
2cis240°
2(-1)
-1-51 3. 2ci8330°
24-0
and
23.
1222 are the required roots.
Argand Disgram showing the fourth roots.
3. Given z còs9+isinə,
cose-isine
(a)
(2 + 2) 3
+3222+z3 z3+z3+3zē (z+7) On substitution, we have (2ce80)3¬(cos0+isine) 3.
ciso
cis72
0.309+0.9511
when n
2,
cis1440
8cos
-0.80940.5881
when
3:
cia216
-0.809-0.5881
when n
Cox30
cis2889
0.309-0.9511.
and
(b) (z-z)3-
Argund Di
the roots of z5,
roots PATTERfifth
(b) The cube roots of -81
ALSO!
-8i
8(-1)
8cis(360n° 270°)
ci s ( 360n° +
2cis(120n® +90°)
ere when n
when
0, 1, 2.
is90o 042
2cis2100
2(-0.866-0.51) -1-732-1
when n 2,
2eis530o.
» 2(0.866-0.51 );
- 1,732–1
211 22 are the
where
required ro
(cose-isine), 3(1)(2cose)
(as 22-1)
cos30+1sin30+ cos30-isin30+ bcose by De Moivre's Theorem 2cos30+6cosü
4cos 0-3cos8.
Ans.
-387(z-z)
..(2ísine)3 = (cose+isine)}
- (cose-isinə)? −3(1)(2isinə
-8isin Özcos30+isin30-
cos30+isin30–
6sine
=2isin30-6isine
sin30-3sin0-4sin 0 Ans.
5z2Z+10231⁄22.
(z+2)5
10 z2 235 z 2 +z5
5zZ
1022z2 (2+2)
~(cose+isine)5.
(cose-isine)5,
5(1)[(cose. isine)2+(cose+ isine)3]+10(1) 2 (2c0a0)
32coa Oscos50+isin50+
cos50-isin50. 5(cos0+isin3p+ cos30-isin30)+ 20cose. -2cos50+10cos304
20cose
cog50=16cos 0-10cos8-
5co830
-16cos 8-10c080- 5(4cos30-3cose) -16cos30-20cos Dr
5cose.
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)及甩括如下:
一睹·五——二七〇二七六。
CT 香港金箜九十九樂◎大厦地下,一
Ans.
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HISTORY (16).
Philip Y. L. Woo
MILL & DALE PRESS LTD.
In the following, we are going to look at the background of the Second World War (1939-1945). Pernaps many of the topics between the two world wars (1919-1939) you have learnt. But it is one thing to know about these topics (like the rise if Nazism in Germany) and
another thing to be able to relate them to the outbreak of the war itself.
BACKGROUND OF THE SECOND WORLD WAR
1. Defects of the First World
War settlement - Many of the problems facing Europe were still unsolved after the First. World War, such as:
a. Germany felt that she was
unjustly treated by the Versailles peace conference of 1919. When Hitler: claimed to revive German power, many Germans listened to him, expecting that he could undo the
humiliation of 1919,
b. The traditional balance of power between the great powers was destroyed, but a new international order that guaranteed peace was absent. The fall of the Austrian Empire in East Europe was followed by the rise of small, independent but weak states. They could be easily conquered by
agressors, especially when Soviet Russia (which
replaced the fallen Tsarist government of pre-1917)
did not cooperate with the Western powers like France in foreign policy.
c. Before the First World War,
Europeans were often
optimistic about their
culture. After 1919,
because of the harmful
effects of the First World War, they began to become pessimistic about International peace and, above all, to fear the coming of another equally destructive war. Many people of the allies (such as France and Britain) wanted to prevent war at all cost. Dictators like Hitler and Mussolini knew this well, and made good use of the fear to commit aggressions, d. Economies were disrupted by the First World War. This led up to, in part at least, the Great Depression of 1929-30. The Great. Depression had two important effects:
I. It led to the rise of Hitler
in Germany.
ii. Its harmful effects
preoccupied Western powers like France and Britain and made them more and more unable to take positive steps to check agg essions.......
13.
作鵝
心欣仙於生
日期星
日五廿月一年一八九一圈公年十七國民唯中
2. From 1919 to 1929, Europe
slowly recovered from the First World War. But the peace was actually unreal, as later events were to show.
3. From 1930 to 1939, Europe gradually stepped into war. a. After the Great Depression, the allied powers became concerned about their only interests only, rather than cooperating with each other to safeguard peace.
b. Fascist Italy and Nazist
Germany made use of the opportunity to expand their territories.
1. The Italian war against
Abyssinia in 1935.
ii. The German annexation
of Austria in 1938. i. The German threat to Czechoslovakia in 1938-39.
The German threat to Poland in 1939.
At first, the allied powers. (Britain and France) tolerated the aggressions. One of the reasons was tha people felt the Versailles treaty with Germany to be really unjust. The powers hoped to satisfy Germany with gains so that peace could be maintained. Historians call this "appeasement", which means trying to peace. dictators.
d. In the end, in 1939, it
became clear that further appeasement was useless. Thus war broken out
between Germeny and powers like Britain and
France. This marked the
outbreak of the Second World War.
1981
中學會考試題預習專欄
經濟
(十六)
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Economics (16)
K. K. Wong & L. T. Chan "MILL & DALE PRESS LTD,
Population:
III: Effects of rapid growth of
population on the society of Hong Kong:
Hong Kong's rapid growth of population since the Second World War has resulted in the following social problems:-
Land and Housing:
Dense population in urban areas has made rent creeping and the supply of houses insufficient. Therefore, overcrowdedness, unhealthy squatters and tenancy.. disputes arise.
b. Health and Environment:
Due to overconcentration of population in urban areas, space for public amenities and medical facilities have long been felt insufficient. Moreover, industrial growth has made many residential and industrial buildings mixed
together. All these result in
五麻加公游
pollution and traffic
congestion,
Social Welfare:
As a result of increasing population, the need for social welfare services arises. Social problems such as crime, drug addiction, family problems, and juvenile delinquency are thus created. IV. Reasons for the population
control in Hong Kong
Population control is Significantly important in Hong Kong for the following
а.
reasons:
On the negative side of population growth, it can be an impediment to economic progress. It poses a heavy burden on the community in the sense that the provision of adequate employment for a growing labour force can be difficult, and that resources for economic development may be diverted to meet the immediate demands of an increasing number of people for basic goods and services, such as foodstuffs, housing, education, medical
care, transportation, etc..
b. As population grows rapidly, per capital income may be reduced. This means that the income earned by each individual falls since the Gross National Product will be shared by a greater population size.
c. Unlike most Asain countries, Hong Kong is characterized by an extreme shortage of natural resources. Population control is necessary to
reduce the growth rate of
demand for foodstuffs and
other necessities,
d. In the past few years, Hong
Kong has experienced a rapid
process of industrilization and becomes an
export-oriented place. But
Inevitably Hong Kong has lost
her comparative advantage in labour-intensive products because of rising wages at
home. The only beneficial way
to maintain her export's
competitiveness in overseas markets is to improve the labour skills and industrial technology. To achieve this, a good human capital must be improved. Thus it is necessary to have adequate. training programmes for the
young generation, while at the same time population control is essential.
e.. In recent years, Hong Kong
has experienced serious Inflation which adds difficulty to her export sector. To curb inflation, one of the effective way is to control the rate of increase of demand for foodstuffs and necessities by keeping down the growth rate of population. f. Population control in Hong
Kong can ease the burden on the government in providing economic, social, and administrative services to the community, thus releasing public funds for the improvement of the economy and assistance to industry.
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