Washing machine is a very popular household appliance, which brings great convenience to people's lives. In terms of working methods, there are several types of household washing machines, such as pulsator, drum type and stirring type. On this basis, various manufacturers have also introduced a variety of specific schemes, designed different geometric and operating parameters, such as the shape of impeller, the shape of inner wall of inner cylinder, rotation mode and speed. Different design schemes have different cleaning efficiency and damage degree.

The first stage problem:

1. Please establish a reasonable index to measure the washing efficiency of the washing machine and the degree of damage to clothes.

2. Please establish a reasonable mathematical model, analyze the working modes of typical pulsator and drum household washing machines, and estimate the cleaning efficiency and damage degree of these two working modes respectively. For the sake of simplicity, we can only consider the washing process, ignoring the rinsing and dehydration process. ; .

Question B: Look at the world with low resolution.

Digital camera technology is widely used in many occasions. Sometimes, due to the limitation of objective conditions, shooting equipment can only image at low resolution. For simplicity, we only consider monochromatic imaging. Assuming that the resolution of imaging is 32.64, the imaging method is to divide the whole rectangular field of view into 32.64 rectangular grids with the same size, and the value of each pixel in the image is the average brightness of the corresponding grid. Every once in a while, an image is taken, and the moving image is reflected as a series of images.

The first stage problem:

Now the whole field of vision is slowly moving in a certain direction, and a series of captured images are transmitted to the computer in real time. Please establish a reasonable mathematical model and algorithm, and use as little time as possible to determine the direction of motion by analyzing real-time images.

Question C: How to effectively curb the occurrence of school bullying?

In recent years, many school bullying events in China have attracted the attention of many people in China under the media reports. Bullying has a very serious and long-term impact on students' physical and mental health, so we should attach great importance to these situations. Bullying is one of the various forms of school violence, and in a sense, it is also a high degree of harm. Unlike occasional violent incidents, bullying is usually accompanied by physical and mental injuries, which usually last for a long time and sometimes may cause lifelong trauma to the victim's mind. If there is no professional psychological guidance, the victim may become a person who retaliates against the society, and then from the victim to the perpetrator, passing on his experience to others intact or magnified 100 times.

On June 2 1 2005, a video of "Pupils being beaten by many people" was widely spread on the Internet. According to netizens, several junior high school students in qingyuan county, Lishui City, Zhejiang Province locked a first-grade pupil in a dark room, violently beat him and burned the child with cigarette butts. Chen Kun, a famous actor, forwarded this video on Weibo at around 8 pm on June 2/KLOC-0. The media person "Dapeng sees the world" also called on the public security department to intervene immediately at the Weibo that night. "Don't be soft, such incidents must be severely punished, and the results will be widely announced!" The attention of many network "big V" made this event quickly ferment into a hot spot. Many netizens were shocked by the scene in the video and lamented that "school bullying phenomenon is so serious". The rapid development of science and technology and the popularity of the Internet have not only brought positive effects to teenagers. Many junior high school students said that they were affected by new violence such as abuse and insult on mobile phones and the Internet. The violent behavior of cyber bullying has caused more direct harm because of the rapid spread of insulting information. In addition, the speed of information dissemination is extremely fast, and it is often too late to stop the spread of information and protect students, which has caused great harm to the victims. There are many reasons that drive teenagers to commit cyber violence, but the main inducement is age. Teenagers do harm to themselves and others because they are young, immature and do not know how to deal with and transform violent impulses. We designed a questionnaire survey aimed at the psychological status of teenagers of different ages, trying to establish a model to judge the possibility that teenagers have some potential psychological problems. The survey is divided into five age groups, involving life education, lifestyle and entertainment, including positive and negative frames respectively. Among them, the dependent variable is designed as an alternative evaluation variable, represented by A or B, and the independent variables include risk preference, cognitive needs (including 18 questions) and decision-making style (including rationality, intuition, dependence, avoidance and impulsiveness, with five questions in each dimension). According to the selected answers of each question, the corresponding scores can be calculated. See annex I for the survey results. ..

The first stage problem:

1. Please judge whether there are significant differences in mental state of different age groups through statistical analysis.

2. Please establish a reasonable mathematical model and analyze the main influencing factors of different frameworks. And write an analysis report of about 500 words to the local newspaper, explaining your main strategy to contain school bullying.