I was invited to a cookout on an old friend’s farm in western Washington. I parked my car outside the farm and walked past a milking house which had apparently not been used in many years. A noise at a window caught my attention, so I entered it. It was a hummingbird (蜂鸟), desperately trying to escape. She was covered in spider-webs (蛛网) and was barely able to move her wings. She ceased her struggle the instant I picked her up.
With the bird in my cupped hand, I looked around to see how she had gotten in. The broken window glass was the likely answer. I stuffed a piece of cloth into the hole and took her outside, closing the door securely behind me.
When I opened my hand, the bird did not fly away; she sat looking at me with her bright eyes. I removed the sticky spider-webs that covered her head and wings. Still, she made no attempt to fly. Perhaps she had been struggling against the window too long and was too tired? Or too thirsty?
As I carried her up the blackberry-lined path toward my car where I kept a water bottle, she began to move. I stopped, and she soon took wing but did not immediately fly away.
Hovering (悬停), she approached within six inches of my face. For a very long moment, this tiny creature looked into my eyes, turning her head from side to side. Then she flew quickly out of sight.
During the cookout, I told my hosts about the hummingbird incident. They promised to fix the window. As I was departing, my friends walked me to my car. I was standing by the car when a hummingbird flew to the center of our group and began hovering. She turned from person to person until she came to me. She again looked directly into my eyes, then let out a squeaking call and was gone. For a moment, all were speechless. Then someone said, “She must have come to say goodbye.”
A few weeks later, I went to the farm again.
I was just about to leave when the hummingbird appeared.
“Sun, sun, sun, here it comes…”
Danny sang while his fingers pressed and pulled skillfully at the guitar strings, delivering a slow and peaceful tune. A circle of audience had formed, nodding and moving slowly to the song.
Lying at the feet of the street performer was his most adoring fan: One-Eyed, a white stray (流浪) dog with pieces of brown. Danny felt the name was suitable considering its physical disability. Usually, One-Eyed would bark loudly as Danny performed. Much to his annoyance, people often mistook the pair as owner and pet. At this time, Danny would reply, “My dog? No!”, eyes rolling at the idea. How he wished the dog would leave him alone instead!
On a snowy night, while Danny was performing, a bird flew downward, landing into the midst of the crowd. It cooed happily as if to harmonize with Danny. Unfortunately, that did not sit well with One-Eyed, which immediately bounced at it and the bird flew away desperately.
The unexpected chaos upturned Danny's hat, which could have been filled with notes and coins from his appreciative audience, leaving it ignored on the ground. "Argh! The hateful dog!” Danny broke down, thinking to himself, “Either the dog goes or I go!”
On the next night, Danny tried to find a new place and chanced upon the park. For a while his earnings were good unsurprisingly as there was a steady flow of visitors. However, that didn't last long. One-Eyed came along and appointed itself as Danny's guardian. "Argh! Here comes the hateful dog again!" That night, Danny hadn't made enough money he should have, all thanks to the troublesome dog.
Danny was almost mad with One-Eyed. “What should I do? Call an animal shelter?” Torn by this problem, he walked aimlessly by the lake of the park. With all his mind focused on how to get rid of the dog, Danny didn't watch his steps. Suddenly, he slipped and fell into the lake accidentally. Struggling in the icy water, he cried for help desperately, almost choking to death. Sensing the approach of death, Danny got into overwhelming panic.
Just then, a familiar barking was heard in the distance.
“My hero! Thank you for saving me,” Danny said gratefully with watery eyes.
的细线（质量不计）一端被固定在架子上，另一端悬挂一个质量为
的物体（可视为质点）。现使物体在水平面做匀速圆周运动，此时细线与竖直方向夹角为
。一段时间后悬挂物体的细线断裂，物体沿水平方向飞出，恰好无碰撞地从传送带最上端（传送轮大小不计）沿传送方向进入传送带。倾角为
的传送带以恒定的速率
沿顺时针方向运行，物体在传送带上经过一段时间从传送带底部离开传送带。已知传送带长度为
，物体和传送带之间的动摩擦因数为
。质量为
的无动力小车静止于光滑水平面上，小车上表面光滑且由水平轨道与
圆轨道平滑连接组成，圆轨道半径为
。物体离开传送带后沿水平方向冲上小车（物体从离开传送带到冲上小车过程无动能损耗），并在小车右侧的最高点离开小车，过一段时间后重新回到小车，不计空气阻力。重力加速度取
。
，
，则下列说法正确的是
；
在定义域内单调，则
；
，则
恒成立；
，则的所有零点之和为0． 如图弧线MN为晨昏线的局部，MN弧度跨越经度90°，此时北京时间为6点，太阳光从M点正北射来，该日M点昼达一年中最长，M、N两点的正午太阳高度差为30°，完成下面小题。
| A．此日太阳直射点北移 | B．地球公转速度较快 |
| C．N点位于北京正南 | D．MN的纬度差为70° |
| A．地处苔原带 | B．位于南极洲 |
| C．极光终年可见 | D．极昼长达半年 |
沙火山是在特殊的地质环境中，沉积后尚未固结的砂体在外部动力干扰下发生液化、流化，砂体喷出地表后形成的地貌。山东省H市某小型河流的一段河床，上下游河床偏高，中间偏低。2019年春季，当地居民对该河段进行清淤，夏季该地区河床上出现大量沙火山。据研究，该地沙火山在不同阶段火山口溢出的水流特征有明显的差异，该类沙火山不易保存，地层中该类型的沙火山可很好的指示水环境状况。下图分别为沙火山不同演化阶段示意图，据此完成下面小题。
| A．a阶段溢出浑水，为沙火山生长阶段 | B．a阶段溢出清水，为沙火山消亡阶段 |
| C．b阶段溢出浑水，为沙火山消亡阶段 | D．b阶段溢出清水，为沙火山生长阶段 |
| A．河流流量增大 | B．河道侵蚀增强 | C．上层泥岩变厚 | D．地下水位上升 |
| A．河流含沙量大 | B．地表水缺乏 | C．地表径流极慢 | D．地下水丰富 |
我国某中学生发现，在书桌的固定观测点上，每年仅有一天通过窗户既可观察到日出也可看到日落。图为该日日出、日落的位置示意图。据此完成下面小题。
| A．大连正值樱花盛开 | B．该地日出方位全年最偏北 |
| C．该地昼长全年最长 | D．沈阳正午日影全年最长 |
| A．上海 | B．沈阳 | C．成都 | D．拉萨 |
的四个顶点都在函数
的图象上，则此正方形的面积为
的函数
.
在
上为单调递增函数；
有四个不相等的实根，在
上是否存在实数
，
，使得函数
在区间
上单调，且的取值范围为
？若存在，求
的取值范围；若不存在，请说明理由． 
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