OpenLLM-France/wikimedia huggingface dataset:
# Calculus Course/Differential Equations/1st Order Differential Equations
## 1st Order Differential Equations

A 1st order differential equation has the form shown below
    $A{\frac {d}{dx}}f(x)+B=0$
It can be shown that roots o the differential equation above is
    $f(x)=Ae^{-\alpha x)$
    $\alpha ={\frac {B}{A}}$

## Proof

The above equation can be rewritten as
    ${\frac {df(x)}{dx}}+{\frac {B}{A}}f(x)=0$
Then
    ${\frac {df(x)}{dx}}=-{\frac {B}{A}}f(x)$
    $\int {\frac {df(x)}{f(x)}}=-{\frac {B}{A}}\int dx$
    $Lnf(x)=-{\frac {B}{A}}x+C$
    $f(x)=e^{-{\frac {B}{A}}x+C)$
    $f(x)=Ae^{-{\frac {B}{A}}x)$

## Summary

First ordered differential equation of the form
    $A{\frac {d}{dx}}f(x)+B=0$
has a exponential root of the form
    $f(x)=e^{-\alpha x+c)$
where
    $\alpha x={\frac {B}{A}}$
    $A=e^{c}$
or
    $f(x)=Ae^{-\alpha x)$
# Calculus Course/Differential Equations/2nd Order Differential Equations
## 2nd Order Differential Equation

2nd Order Differential Equation is an equation that has the general form
    $a{\frac {d^{2}}{dx^{2}}}f(x)+b{\frac {d}{dx}}f(x)+c=0$

## Characteristic Equation

2nd Order Differential Equations above can be rewritten as shown
    ${\frac {d^{2}}{dx^{2}}}f(x)+{\frac {b}{a}}{\frac {d}{dx}}f(x)+{\frac {c}{a}}=0$
Let
    $s={\frac {d}{dx}}$
Then
    $s^{2}+{\frac {b}{a}}s+{\frac {c}{a}}=0$
    $s=(-\alpha \pm {\sqrt {\lambda }}$) t
    $\alpha ={\frac {b}{2a}}$
    $\beta ={\frac {c}{a}}$
    $\lambda ={\sqrt {\alpha ^{2}-\beta ^{2}}}$

### Case 1

When
    $\lambda =0$
Then
    $\alpha ^{2}=\beta ^{2}$
    $s=e^{-\alpha t)$
Equation has one real roots

### Case 2

When
    $\lambda >0$
Then
    $\alpha ^{2}>\beta ^{2}$
    $s=e^{-\alpha x)e^{\pm (\lambda x)]$
Equation has two real roots

### Case 3

When
    $\lambda <0$
Then
    $\alpha ^{2}<\beta ^{2}$
    $s=e^{-\alpha t)[e^{\pm j\lambda t)]$
Equation has two compex roots

## Special Case
### Case 1

Differential Equation of the form
    ${\frac {d^{2}f(t)}{dt^{2}}}+\lambda =0$
    $s^{2}=-\lambda$
Roots of equation
    $s=\pm j{\sqrt {\lambda }}$

### Case 2

Differential Equation of the form
    ${\frac {d^{2}f(t)}{dt^{2}}}-\lambda =0$
    $s^{2}=\lambda$
Roots of equation
    $s=\pm {\sqrt {\lambda }}$

## Summary

2nd Order Differential Equation
    ${\frac {d^{2}}{dx^{2}}}f(x)+{\frac {b}{a}}{\frac {d}{dx}}f(x)+{\frac {c}{a}}=0$
has roots depend on the value of $\lambda$
* $\lambda =0.f(x)=e^{-\alpha x)$
* $\lambda >0.f(x)=e^{-\alpha x)e^{\pm \lambda x)$
* $\lambda <0.f(x)=e^{-\alpha x)e^{\pm j\lambda x)$
With
    $\alpha ={\frac {b}{a}}$
    $\beta ={\frac {c}{a}}$
    $\lambda ={\sqrt {\alpha ^{2}-\beta ^{2}}}$
# Calculus Course/Rate of Change
## Rate of Change

Rate of Change is used to describe the ratio of a change in one variable compare to a change of another variable
If there is a function $f(x)=y$ then the rate of change of the function $f(x)$ correspond to the rate of change of variable z is
    ${\frac {\Delta y}{\Delta x}}={\frac {\Delta f(x)}{\Delta x}}$

## Example

If there are two points $(1,3)$ and $(2,7)$
    ${\frac {\Delta y}{\Delta x}}={\frac {\Delta f(x)}{\Delta x}}={\frac {7-3}{2-1}}=4$
# Chinese (Mandarin)/Traditional/Commodities

| Mandarin - Traditional Han character 漢字 - 繁體字/正體字/傳統漢字 | Hanyu Pinyin 漢語拼音 | English 英語 |
| 洗髮露 | xǐfàlù | Shampoo |
| 沐浴露 | mùyùlù | Body Wash |
| 洗衣粉 | xǐyīfěn | Washing powder |
| 漂白液 | piǎobáiyè | Bleach |
# Chinese (Mandarin)/Traditional/Family

| Mandarin - Traditional Han character 漢字 - 繁體字/正體字/傳統漢字 | Hanyu Pinyin 漢語拼音 | English 英語 |
| 阿姨；姨媽 | āyí; yímā | mother's sister |
| 爸爸 | bà ba | dad |
| 表弟 | biǎo dì | younger male cousin with different last name |
| 表哥 | biǎo gē | older male cousin with different last name |
| 表姐 | biǎo jiě | older female cousin with different last name |
| 表妹 | biǎo mèi | younger female cousin with different last name |
| 伯父 | bó fù | father's older brother |
| 伯母 | bó mǔ | father's older brother wife |
| 弟弟 | dì di | younger brother |
| 弟媳 | dì xí | younger brother's wife |
| 兒子 | ér zi | son |
| 父母 | fù mǔ | parents |
| 父親 | fù qin | father |
| 哥哥 | gē ge | older brother |
| 姑媽 | gū mā | father's sister |
| 姑丈 | gū zhàng | father's sister's husband |
| 孩子 | hái zi | children |
| 姐夫 | jiě fu | older sister's husband |
| 姐姐 | jiě jie | older sister |
| 舅舅 | jiù jiu | mother's brother |
| 舅媽 | jiù mā | mother's brother wife |
| 媽媽 | mā ma | mother |
| 妹妹 | mèi mei | younger sister |
| 妹婿 | mèi xù | younger sister's husband |
| 母親 | mǔ qīn | mother |
| 女兒 | nǚ ér | daughter |
| 妻子 | qī zi | wife |
| 嫂嫂 | sǎo sao | older brother's wife |
| 嬸嬸 | shěn shěn | father's younger brother's wife |
| 叔父 | shū fù | father's younger brother |
| 雙胞胎 | shuāng bāo tāi | twin |
| 堂弟 | táng dì | younger male cousin with same last name |
| 堂哥 | táng gē | older male cousin with same last name |
| 堂姐 | táng jiě | older female cousin with same last name |
| 堂妹 | táng mèi | younger female cousin with same last name |
| 外公 | wài gōng | mother's father |
| 外婆 | wài pó | mother's mother |
| 外甥 | wài shēng | sister's son |
| 外甥女 | wài shēng nǚ | sister's daughter |
| 爺爺 | yé ye | grandfather (father's side) |
| 奶奶 | nǎi nai | grandmother (father's side) |
| 姥爺 | lǎo yé | grandfather (mother's side) |
| 姥姥 | lǎo lao | grandmother (mother's side) |
| 姨丈 | yí zhàng | mother's sister husband |
| 丈夫 | zhàng fu | husband |
| 侄女 | zhí nǚ | brother's daughter |
| 侄子 | zhí zi | brother's son |
| 祖父 | zǔ fù | father's father |
| 祖母 | zǔ mǔ | father's mother |
| 曾祖父 | zēng zǔ fù | father's grandfather (also called great-grandfather) |
| 曾祖母 | zēng zǔ mǔ | father's grandmother (great-grandmother) |
# Chinese (Mandarin)/Traditional/Lesson 5

| Lessons: | Main - Pron. - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 |
| Subpages: | Simplified - Exercises - Stroke Order |

# Lesson 5: Measure words
### Measure Words/量詞（liang4ci2)

1. 這本書裡沒有一個漢字。
    Zhè bĕn shū lǐ méi yǒu yí gè Hànzì.
    This book doesn’t contain one Chinese character.
2. 那間宿舍裡有六十個學生。
    Nà jiān sùshè lǐ yǒu liùshí ge xuésheng.
    That dorm has sixty students.

#### Some Common Measure Words

| Character | Pinyin | Main uses | Example |
| 個 (个) | ge (gè) | individual things, people — usage of this classifier in conjunction with any noun is generally accepted if the person does not know the proper classifier. | 一個書包 yí gè shū bāo |
| 箇 | gè | general classifier |
| 把 | bǎ | "handful" — objects that can be held (knives, keys; also chairs) | 一把刀 yì bă dāo. One knife. (The official measure word for scissors is "把", however, many Chinese use "个" when speaking. In written Chinese however, people usually revert to "把".) |
| 包 | bāo | "package", "bundle" |
| 杯 | bēi | "cup" — drinks |
| 本 | běn | "volume" — bound print matter (books, etc.) |
| 冊 (册) | cè | volumes of books |
| 次 | cì | "time" — opportunities, accidents |
| 滴 | dī | "droplet" water, blood, and other such fluids |
| 點 (点) | diǎn | ideas, suggestions, can also mean "a bit" |
| 朵 | duǒ | flowers, clouds | 一朵花 yì duŏ huā. One flower. |
| 根 | gēn | thin, slender objects (needles, pillars, etc.) |
| 家 | jiā | gathering of people (families, companies, etc.) |
| 件 | jiàn | matters, clothing, etc. | 一件衣服 yí jiàn yī fù |
| 節 (节) | jié | "section" — of bamboo, classes, etc. |
| 口 | kǒu | people in a family, population of a place |
| 輛 (辆) | liàng | automobiles, bicycles, etc. | 一輛車 yí liàng chē. One car. |
| 面 | miàn | flat and smooth objects (mirrors, flags, etc.) |
| 匹 | pǐ | horses and other mounts, rolls/bolts of cloth | 一匹馬 yì pǐ mă. One horse. |
| 片 | piàn | "slice" — flat objects, cards, slices of bread, etc. |
| 瓶 | píng | "bottle" — drinks |
| 艘 | sōu | ships | 一艘船 yì sōu chuán. One boat. |
| 所 | suǒ | buildings | 一所學校 yi suo3 she2 siao4 |
| 臺 (台) | tái | heavy objects (TVs, computers, etc.) and performances (theatre, etc.) | 一臺電視 yi tai2 dien4 si4 |
| 條 (条) | tiáo | long, narrow, flexible objects (fish, trousers, etc.) | 一條魚 yì tiáo yú. One fish. |
| 頭 (头) | tóu | "head" — certain animals (pigs, cows, etc.), hair | 一頭牛 yì tóu niú. One head of cattle. |
| 位 | wèi | polite classifier for people |
| 張 (张) | zhāng | "sheet" — flat objects (paper, tables, etc.), faces, bows, paintings, tickets, constellations | 一張紙 yì zhāng zhĭ. One piece of paper. |
| 支 | zhī | stick-like objects (pens, chopsticks, etc.) |
| 隻 (只) | zhī | one of a pair, animals (birds, cats, etc.) | 一只狗 yì zhī gŏu. One dog. |
| 種 (种) | zhǒng | types or kinds of objects |
A more complete reference list of Chinese measure words can be found in the Wikipedia.
| Lessons: | Main - Pron. - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 |
| Subpages: | Simplified - Exercises - Stroke Order |
# Chinese (Mandarin)/Traditional

Welcome to the Mandarin Wikibook, a free Chinese textbook on the Standard Mandarin dialect. This page links to lessons using Traditional Han characters 繁體中文 (used in Taiwan, Macau and Hong Kong). There is also a Simplified Han Character Version 简体中文 available (used in mainland China).
* 我們需要您的幫助，如果您熟悉中文，請協助編撰本教科書。 我们需要您的帮助！如果您熟悉中文，请协助编撰本教科书。

## Lessons / 課程

| Introduction / 介紹 About Mandarin 中文是什麽？ How to use this textbook 如何使用本教科書 How to study Mandarin 如何學中文？ Pronunciation / 發音 Pinyin Pronunciation Basics 基礎拼音發音入門 Pronunciation of Initials Pronunciation of Finals Using Tones 使用聲調 More About Hanyu Pinyin Vocabulary 生字/字彙 Part 1: Family 第一部分：家庭 Part 2: Commodity 第二部分：日用品 Part 3: Transport 第三部分：交通 Part 4: Food 第四部分：食物 Part 5: Animals 第五部分：動物 | Lesson Texts / 課文 Lesson 1: Hello! 第一課：你好！ Lesson 2: Are you busy today? 第二課：今天你忙不忙? Lesson 3: An introduction to particles 第三課：助詞 Lesson 4: Word order and Verbs 第四課：詞序和動詞 Lesson 5: Measure words 第五課：量詞 Lesson 6: More on interrogatives 第六課：疑問助詞 Lesson 7: What's this? 第七課：這是什麽？ Lesson 8: My name is Wang Ming 第八課：我的名字叫王明。 Lesson 9: Where is the railway station? 第九課：火車站在哪裡？ Lesson 10: A telephone conversation 第十課：電話 Lesson 11: Taiwan 第十一課：臺灣 Lesson 12: Mandarin is so interesting! 第十二課：漢語真有趣 Lesson 13: I'm sick 第十三課：我生病了 Lesson 14: Drinking tea 第十四課：喝茶 Lesson 15: China 第十五課：中國 Lesson 16: Basic Chinese History 第十六課：基本中國歷史 |

## Appendices / 附錄

| Mandarin-English Dictionary 漢英字典 English-Mandarin Dictionary 英漢字典 Greetings 問候語 Possible Initial-Final Combinations Numbers 數字 | Nations of the World 世界各國 Radicals 部首 Slang 俚語 Web Resources 中文網路資源 |

### Related Books 相關書籍

* Written Chinese
* Guide to Writing East Asian Languages 漢字書寫
* Cantonese (Yue) 廣東話（粵語）
* Chinese Phrasebook (on WikiVoyage)
* Taiwanese (Southern Min / Min Nan) 臺語（閩南語）
* Cookbook:Cuisine of China

## Contributors

* Contributor's Guide
* Textbook Planning 課文安排
* Development History
* Contributors 撰文者
# Chinese (Mandarin)/Traditional/Animals

| Mandarin - Traditional Han character 漢字 - 繁體字/正體字/傳統漢字 | Mandarin - Simplified Han character 汉字 - 简化字 | Hanyu Pinyin 漢語拼音 / 汉语拼音 | English 英語 / 英语 |
| 斑馬 | 斑马 | bān mǎ | zebra |
| 蝙蝠 | 蝙蝠 | biān fú | bat |
| 蒼蠅 | 苍蝇 | cāng ying | fly |
| 長頸鹿 | 长颈鹿 | cháng jǐng lù | giraffe |
| 臭鼬 | 臭鼬 | chòu yòu | skunk |
| 刺蝟 | 刺蝟 | cì wèi | hedgehog |
| 大老鼠 | 大老鼠 | dà lǎo shǔ | rat |
| 大象 | 大象 | dà xiàng | elephant |
| 袋鼠 | 袋鼠 | dài shǔ | kangaroo |
| 鵝 | 鹅 | é | goose |
| 鱷魚 | 鳄鱼 | è yú | alligator |
| 鴿子 | 鸽子 | gē zi | pigeon |
| 公牛 | 公牛 | gōng niú | bull |
| 狗 | 狗 | gǒu | dog |
| 河狸 | 河狸 | hé lí | beaver |
| 河馬 | 河马 | hé mǎ | hippopotamus |
| 河豚 | 河豚 | hé tún | pufferfish |
| 海豚 | 海豚 | hái tún | dolphin |
| 黑豹 | 黑豹 | hēi bào | panther |
| 猴子 | 猴子 | hóu zi | monkey |
| 蝴蝶 | 蝴蝶 | hú dié | butterfly |
| 胡蜂 | 胡蜂 | hú fēng | wasp |
| 狐狸 | 狐狸 | hú li | fox |
| 火雞 | 火鸡 | huǒ jī | turkey |
| 雞 | 鸡 | jī | chicken |
| 鯨魚 | 鲸鱼 | jīng yú | whale |
| 孔雀 | 孔雀 | kǒng què | peacock |
| 狼 | 狼 | láng | wolf |
| 老虎 | 老虎 | lǎo hǔ | tiger |
| 老鼠 | 老鼠 | lǎo shǔ | mouse |
| 龍蝦 | 龙虾 | lóng xiā | lobster |
| 驢子 | 驴子 | lǘ zi | donkey |
| 駱駝 | 骆驼 | luò tu | camel |
| 馬 | 马 | mǎ | horse |
| 螞蟻 | 蚂蚁 | mǎ yǐ | ant |
| 貓 | 猫 | māo | cat |
| 蜜蜂 | 蜜蜂 | mì fēng | bee |
| 鳥 | 鸟 | niǎo | bird |
| 牛 | 牛 | niú | cow |
| 螃蟹 | 螃蟹 | páng xiè | crab |
| 企鵝 | 企鹅 | qǐ é | penguin |
| 蜻蜓 | 蜻蜓 | qīng tíng | dragonfly |
| 青蛙 | 青蛙 | qīng wā | frog |
| 鯊魚 | 鲨鱼 | shā yú | shark |
| 山羊 | 山羊 | shān yáng | goat |
| 蛇 | 蛇 | shé | snake |
| 獅子 | 狮子 | shī zi | lion |
| 松鼠 | 松鼠 | sōng shǔ | squirrel |
| 兔子 | 兔子 | tù zi | rabbit |
| 蚊子 | 蚊子 | wén zi | mosquito |
| 蝸牛 | 蜗牛 | wō niú | snail |
| 烏龜 | 乌龟 | wū guī | turtle |
| 犀牛 | 犀牛 | xī niú | rhinoceros |
| 蝦 | 虾 | xiā | shrimp |
| 熊 | 熊 | xióng | bear |
| 熊貓 | 熊猫 | xióng māo | panda |
| 鴨 | 鸭 | yā | duck |
| 羊 | 羊 | yáng | sheep |
| 鷹 | 鹰 | yīng | eagle |
| 魚 | 鱼 | yú | fish |
| 豬 | 猪 | zhū | pig |
| 烏鴉 | 乌鸦 | wū yā | Crow |
# Chinese (Mandarin)/Traditional/Food

| Mandarin - Traditional Han character 漢字 - 繁體字/正體字/傳統漢字 | Hanyu Pinyin 漢語拼音 | English 英語 |
| 飯* | fàn | food |
| 果 | guǒ | fruit |
| 果汁 | guǒzhī | fruit juice |
| 蘋果 | píngguǒ | apple |
| 香蕉 | xiāngjiāo | banana |
| 草莓 | cǎoméi | strawberry |
| 芒果 | mángguǒ | mango |
| 柳橙 | liǔchéng | orange |
| 楊桃 | yángtáo | starfruit |
| 漢堡 | hànbǎo | hamburger |
| 三明治/三文治 | sānmíngzhì/sānwénzhì | sandwich |
| 豬肉 | zhūròu | pork |
| 雞肉 | jīròu | chicken |
| 牛肉 | niúròu | beef |
| 羊肉 | yángròu | mutton |
| 魚肉 | yúròu | fish (as meat) |
| 湯 | tāng | soup |
| 麵包 | miànbāo | bread |
| 雞蛋 | jīdàn | egg |
| 米飯 | mǐfàn | rice |
| 麵條 | miàntiáo | noodles |
    $^*$ Depending on context, 飯 can have a different meaning. 一碗飯 means a bowl of rice.
# Chinese (Mandarin)/Traditional/Lesson 3

| Lessons: | Main - Pron. - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 |
| Subpages: | Simplified - Exercises - Stroke Order |

# Lesson 3: An introduction to particles - 第三課：助詞

The Chinese language employs heavy usage of particles to modify the meaning of characters and sentences. Since Chinese has neither inflections nor tense, the mastery of particles is an absolute must if one is to fully comprehend both written and spoken Chinese. Below, you will find some of the most common particles in everyday Chinese.

## The De [的] particle as possessive

* The particle de [的] can be used to indicate possession. It is roughly equivalent to the contraction "X's" in English, where X is the subject.
1. 她的名字是金妮。
    Tā de míngzi shì Jīnní.
    Her name is Ginny.

## The Le/Liăo [了] particle

Perfect Particle, Completive Particle The 了 particle is used mainly to indicate a completed action (in English, this is the perfect aspect).
Example: 他 走 了。 Tā zŏu le. He has gone.
The "le" here is used to modify 走 (zŏu, to go) into an action which has already been completed.
了 can also be used as an imperative, that is, a command which is issued by the subject Example: 別 再 打擾 我 了! Bié zài dărăo wŏ le! Do not bother me again! In this instance, le is used in conjunction with bié ("do not") to form an imperative. Note: most imperatives are not formed using this construction.
Finally, 了, as in Liăo (a homographic variant) can be used to indicate the subject's capability in doing such and such.
Example: 我 實在 吃 不 了 了。 Wŏ shízài chī bù liăo le. I cannot possibly eat any more. At first glance, this sentence may seem a bit daunting as it includes two instances of the le particle, paired side-by-side. However, the first le is understood to be liăo given its placement (bù + le is a nonsensical pairing). Therefore, liăo serves to indicate the capability of eating any further and le emphasizes this assertion.

## The Zhe/Zháo [著] particle

The Zhe/Zháo particle is another particle that you'll frequently encounter in the course of your Chinese studies. Zhe, when added beside a character and thus forming a preposition, is used primarily to indicate an action which is continuous.
Example: 他 睡著覺 時 有人 敲門。 Tā shuìzhe jiào shí yŏurén qiāomén. While he was sleeping, someone knocked on the door.
In addition, Zháo is used to indicate accomplishment.
Example: 我 終於 把 東西 買 著 了! Wŏ zhōngyú bă dōngxī măi zháo le. I've finally been able to buy this item! The bă (noun) (verb) zháo (le) construction is a particularly useful one and should be studied.
# Chinese (Mandarin)/Traditional/Lesson 4

| Lessons: | Main - Pron. - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 |
| Subpages: | Simplified - Exercises - Stroke Order |

# Lesson 4: Word order and Verbs
### Comparisons Using bǐ [比]

1. 她比我忙。
    Tā bǐ wǒ máng.
    She is busier than I am.
2. 東尼也比我忙很多。
    Dōngní yě bǐ wǒ máng hěn duō.
    Tony is also a lot busier than I am.
| Lessons: | Main - Pron. - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 |
| Subpages: | Simplified - Exercises - Stroke Order |
# Canvas 2D Web Apps/Transformable Objects

This chapter introduces “transformable objects.” Here, “transformable objects” denote images that can be moved (“translated”), rotated, and scaled (uniformly in both directions) by two-finger gestures. Transformable objects are used very much like draggable objects; however, their process functions requires another image for the case that they are touched by two fingers and it takes another boolean value to determine whether the object can be dragged with one finger or the mouse (instead of only with two fingers).
As with draggable objects, any number of objects can be transformed simultaneously (as long as the touch device supports the required number of touch events). Moreover, application programmers don't have to worry about the handling of multiple simultaneous touch events: the process function receives only events with a single pair of coordinates and processes only one object at a time.

### The Example

The example of this chapter (which is available online; also as downloadable version) shows two objects: both can be dragged with one finger (or a mouse) and transformed with two fingers but one cannot be scaled and the other cannot be rotated. The following sections discuss how to use transformable objects and how them. See the chapter on draggable objects for other parts.

### Using Transformable Objects

Similarly to draggable object, a global variable should be defined for each transformable object. In the example, this looks like this:
The transformable objects are then processed in the page's process functions:
The last argument of the process function (here it's cuiConstants.isDraggableWithOneFinger | cuiConstants.isTransformableWithTwoFingers) specifies the available forms of interaction. To support multiple forms of interaction, the constants have to be combined with a bitwise-or as in the example. Other useful constants are cuiConstants.isDraggableWithTwoFingers, cuiConstants.isRotatableWithTwoFingers and cuiConstants.isUniformlyScalableWithTwoFingers. Deactivating rotation and scaling with these flags is not as flexible as the method in the example; however, it avoids some translational movement that comes with rotation and scaling gestures.
The function process returns true whenever the object processed the event. In these cases, additional actions should be taken. Here, the scaling of the first object is deactivated by always setting it to 1.0. Analogously, the rotation of the second object is deactivated by always setting the rotation angle to 0 degrees.
Of course, there are many more possibilities of reacting to the transformation of objects; e.g., restricting translationX and translationY.

### Implementation of Transformable Objects

Due to the different transformations and the use of two touch points for the gesture, transformable objects require considerably more properties than draggable objects:
< Canvas 2D Web Apps
# Canvas 2D Web Apps/User Prompts

In HTML5, web apps are allowed to prompt users for input with simple dialog boxes, in particular an alert dialog (message and OK button), a confirm dialog (message, OK, and Cancel button), and a prompt for textual input (message, default text, OK, and Cancel button). W3C has published recommendations for a Web Application API for User prompts. In the Mozilla Developer Network, see the window object (functions alert, confirm, and prompt).
< Canvas 2D Web Apps
# Car Washing Techniques/End Result
## End result

Car-washing is an activity often referenced in movies, songs, and other media. Keeping a clean vehicle goes a long way toward improving the appearance of the vehicle, even if it is a few years old. Regular washing and waxing will prolong the shine of the vehicle's paint.

## Other Resources

* The Auto Detailing Wiki -
* The Detailing FAQ -
# Car Washing Techniques/Equipment
## Equipment

There are a number of items that aid in making car-washing an enjoyable and convenient practice. Old clothes and shoes are recommended in order to avoid soiling preferred clothing. If the weather feels hot then it is preferable to wait until later in the afternoon. The vehicle could also be relocated to a shaded area such as under a tree, but do not leave a clean vehicle under a tree overnight as a combination of tree sap, pollen , and fallen leaves may collect on it. If the weather is too cold, then the risk of contracting hypothermia (or simply experiencing discomfort) exists, and the water may freeze onto the car. Also, if rain is forecasted for when the vehicle is scheduled to be washed or for shortly after, then postpone until the threat of rain has passed. A fresh dose of rain can leave dirt and water spots — grayish circles that form on the vehicle after a rainstorm.
The most common car-washing equipment:
* Two clean buckets. One bucket has the car-washing soap and the other bucket has water for rinsing the sponge in order to avoid washing your car with dirty water.
* A sponge or wash mitt made of thick soft foam (not a dishwashing sponge). Diapers, cloths, shirts, etc. are not recommended.
* Some car-washing soap. Never use dish detergents; they are far too harsh and will strip any applications of wax. Another reason to not use dish or laundry detergent is that they are harder to rinse off with cold water and may therefore leave soap scum behind.
* A water hose that is long enough to reach around the vehicle without having to be draped over the trunk or hood.
* A chamois, which is a super-absorbent cloth that does not leave lint on the vehicle.
* The Auto Detailing Wiki -
* The Detailing FAQ -
* Waterless car cleaners -
# Car Washing Techniques
## Table of Contents

* Cover
* Introduction
* Equipment
* Location
* Procedure
* End Result

## List of authors

* Jaberwocky6669
# Car Washing Techniques/Introduction
## Introduction

Maintaining the surface of your vehicle is as important as maintaining the vehicle's engine. A car that runs great and looks good may actually bring in a higher resale value than a vehicle that runs great but has a poor appearance. A clean vehicle's paint will last longer and need fewer expensive repairs than paint that is allowed to become dull and thin due to oxidation.
In today's modern industrial environment the surface of a vehicle is subjected to daily abuse. The sun beats down on your car all day every day, pollutants and dirt deeply embed themselves into your paint, and minute slivers of metal become lodged into your paint which eventually rust. If you have owned a white vehicle or have observed one then you may have noticed specks of rust. Those metal slivers are the cause.
Car washing techniques vary amongst individual vehicle owners. Car washing is an essential function of preventive maintenance. Keeping the exterior of a vehicle clean prevents rust and oxidation and also reduces the occurrence of fine scratches. This article attempts to relay the most common method and the significance of this pastime. Washing a vehicle with soap and a sponge is not the main body of work. In fact, this is only the preparation for the real cleaning. Soap and sponge will not remove all contaminants from a vehicle's surface. Other products will be required such as clay bars, cleaner wax, polish, etc.
It is recommended that you read the section in your owners manual about washing your car. There you will find specific instructions and cautions for cleaning the equipment in your particular model, such as prohibiting the use of acid based wheel cleaners.
In the next section we discuss the various equipment that you will need.
# Car Washing Techniques/Cover

Welcome to the wikibook for Car Washing Techniques
Proceed to the Table of Contents