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In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
the free encyclopedia that anyone can edit. "Cross Road Blues" is a song written by the American blues artist Robert Johnson. He sang it as a solo piece with acoustic slide guitar in the Delta blues style. The lyrics describe Johnson's grief at being unable to catch a ride at an intersection before the sun sets.
Apollo 11 (July 16–24, 1969) was the American spaceflight that first landed humans on the Moon. Commander Neil Armstrong and Lunar Module Pilot Buzz Aldrin landed the Apollo Lunar Module Eagle on July 20, 1969, at 20:17 UTC, and Armstrong became the first person to step onto the Moon's surface six hours and 39 minutes later, on July 21 at 02: ...
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
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The collection of fortifications known as the Great Wall of China has historically had a number of different names in both Chinese and English. In Chinese histories, the term "Long Wall(s)" (t 長城, s 长城, Chángchéng) appears in Sima Qian's Records of the Grand Historian, where it referred both to the separate great walls built between and north of th...
Early walls
The Chinese were already familiar with the techniques of wall-building by the time of the Spring and Autumn period between the 8th and 5th centuries BC. During this time and the subsequent Warring States period, the states of Qin, Wei, Zhao, Qi, Han, Yan, and Zhongshanall constructed extensive fortifications to defend their own borders. Built to withstand the attack of small arms such as swords and spears, these walls were made mostly of stone or by stamping earth and gravel between board fra...
Ming era
The Great Wall concept was revived again under the Ming in the 14th century, and following the Ming army's defeat by the Oirats in the Battle of Tumu. The Ming had failed to gain a clear upper hand over the Mongol tribes after successive battles, and the long-drawn conflict was taking a toll on the empire. The Ming adopted a new strategy to keep the nomadic tribes out by constructing walls along the northern border of China. Acknowledging the Mongol control established in the Ordos Desert, th...
Foreign accounts
None of the Europeans who visited China or Mongolia in the 13th and 14th centuries, such as Giovanni da Pian del Carpine, William of Rubruck, Marco Polo, Odoric of Pordenone and Giovanni de' Marignolli, mentioned the Great Wall. The North African traveler Ibn Battuta, who also visited China during the Yuan dynasty c.1346, had heard about China's Great Wall, possibly before he had arrived in China. He wrote that the wall is "sixty days' travel" from Zeitun (modern Quanzhou) in his travelogue G...
A formal definition of what constitutes a "Great Wall" has not been agreed upon, making the full course of the Great Wall difficult to describe in its entirety.The defensive lines contain multiple stretches of ramparts, trenches and ditches, as well as individual fortresses. In 2012, based on existing research and the results of a comprehensive map...
Before the use of bricks, the Great Wall was mainly built from rammed earth, stones, and wood. During the Ming, however, bricks were heavily used in many areas of the wall, as were materials such as tiles, lime, and stone. The size and weight of the bricks made them easier to work with than earth and stone, so construction quickened. Additionally, ...
While portions north of Beijing and near tourist centers have been preserved and even extensively renovated, in many other locations the wall is in disrepair. The wall sometimes provided a source of stones to build houses and roads. Sections of the wall are also prone to graffiti and vandalism, while inscribed bricks were pilfered and sold on the m...
Various factoidsin popular culture claim that the Great Wall can be seen (with the naked eye) from space, with questionable degrees of veracity.
The Great Wall at BadalingThe Great Wall at dawnThe Juyongguan area of the Great Wall accepts numerous tourists each day.Remains of Beacon tower, near Yumenguan, 2011International Friends of the Great Wall Archived February 17, 2009, at the Wayback Machine– organization focused on conservationGreat Wall of China on In Our Time at the BBCLyon [c] ( Franco-Provençal: Liyon ), traditionally spelled in English as Lyons, [d] is the third-largest city of France. [e] It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, 391 km (243 mi) southeast of Paris, 278 km (173 mi) north of Marseille, 113 km (70 mi) southwest of Geneva, 58 km (36 ...
Mao Zedong [a] (26 December 1893 – 9 September 1976) was a Chinese politician, Marxist theorist, military strategist, poet, and revolutionary who was the founder of the People's Republic of China (PRC). He led the country from its establishment in 1949 until his death in 1976, while also serving as the chairman of the Chinese Communist Party ...
