One possible version:
June 8, 20xx
Dear Sir,
I'm sorry to tell you that I can't go to school today, I've caught a cold because I swam in the school's swimming pool yesterday.
This morning I had a headache. After taking my temperature, my mother found that I had a high fever, immediately she took me to see a doctor, who advised me to stay in bed for 2 days. Now I am writing to you to ask for 2 days' sick leave.
With best wishes
Your students,
Tom
Dear department:
I was reading a correspondence, in ____ years ____ month ____ to ____ years ____ month ____ day, leave ____ days, please approve.
Dear Mr. Smith，
I would like to apply for an annual leave from January 25th to 31st.
As you may know the Spring Festival is falling on February 1st this year. It's the most important holiday in China and offers the best occasion for family reunion. However, over the past 3 years I missed the reunions due to tight work schedule. Now that I have wrapped up my work for this year, I would like to go back to my hometown to pay filial piety to my parents and help my sole brother prepare his wedding on January 28th.
It's indeed double happiness for my family that I would like to be part of. Coupled with the official holidays for the Spring Festival, I will have two weeks off which will definitely gear me up for better work in the new year. I'm looking forward to your kind answer.
Best regards,
George Chen
Li Wei
An Application For Annual Leave
To: Mr. John Smith, General Manager
From: George Chen, Accounting Department
Date: January 22, 20xx
Subject: Application for annual leave
Dear teacher,
I'm xxx.I'm sorry that I can't go to school today.Because I have a fever.I feel very bad now.So I want to stay at home to take a rest.I hope you can permit me to stay at home.
Yours,
xxx
To: John Smith, Supervisor
From: George Chen, Accounting Department
Date: March 11, 20xxSubject: Casual Leave of Absence
John, I would like to know if I could ask for a casual leave of absence from March 23 to 27.
Yesterday I received a letter from my parents, who are both over 70, telling me that a big flood took place at my home village, causing serious damage to my house. As the only son of my parents, I should of back to assess the situation, and help them to get over these difficulties. Though I cannot stay at home for too long a time, I should at least make arrangements for repair work. I believe my relatives in the village and my neighbors will also come to help. Financially I have no difficulties.
I will call you at 1:30p.m. or you can call me at any time.